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BEGIN:VEVENT
SUMMARY:Salma Kuhlmann (University of Konstanz)
DTSTART:20210113T134500Z
DTEND:20210113T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/1
DESCRIPTION:Title: Strongly NIP almost real closed fields\nby Salma Kuhlmann
(University of Konstanz) as part of Leeds Models and Sets\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rehana Patel (African Institute for Mathematical Sciences Senegal)
DTSTART:20210120T134500Z
DTEND:20210120T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/2
DESCRIPTION:Title: Combining logic and probability in the presence of symmetry\nby Rehana Patel (African Institute for Mathematical Sciences Senegal)
as part of Leeds Models and Sets\n\n\nAbstract\nAmong the many approaches
to combining logic and probability\, an important one has been to assign p
robabilities to formulas of a classical logic\, instantiated from some fix
ed domain\, in a manner that respects logical structure. A natural additio
nal condition is to require that the distribution satisfy the symmetry pro
perty known as exchangeability. In this talk I will trace some of the hist
ory of this line of investigation\, viewing exchangeability from a logical
perspective. I will then report on the current status of a joint programm
e of Ackerman\, Freer and myself on countable exchangeable structures\, ro
unding out a story that has its beginnings in Leeds in 2011.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tin Lok Wong (National University of Singapore)
DTSTART:20210127T114500Z
DTEND:20210127T130000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/3
DESCRIPTION:Title: Arithmetic under negated induction\nby Tin Lok Wong (Nati
onal University of Singapore) as part of Leeds Models and Sets\n\n\nAbstra
ct\nArithmetic generally does not admit any non-trivial quantifier elimina
tion. I will talk about one exception\, where the negation of an induction
axiom is included in the theory. Here the Weak Koenig Lemma from reverse
mathematics arises as a model completion.\nThis work is joint with Marta F
iori-Carones\, Leszek Aleksander Kolodziejczyk and Keita Yokoyama.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynn Scow (California State University\, San Bernardino)
DTSTART:20210203T144500Z
DTEND:20210203T160000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/4
DESCRIPTION:Title: Semi-retractions and preservation of the Ramsey property\
nby Lynn Scow (California State University\, San Bernardino) as part of Le
eds Models and Sets\n\n\nAbstract\nFor structures $A$ and $B$ in possibly
different languages we define what it means for $A$ to be a semi-retractio
n of $B$. An injection $f:A \\rightarrow B$ is quantifier-free type respec
ting if tuples from $A$ that share the same quantifier-free type in $A$ ar
e mapped by $f$ to tuples in $B$ that share the same quantifier-free type
in $B$. We say that $A$ is a semi-retraction of $B$ if there are quantifie
r-free type respecting injections $g: A \\rightarrow B$ and $f: B \\righta
rrow A$ such that $f \\circ g : A \\rightarrow A$ is an embedding.\nWe wil
l talk about examples of semi-retractions and give conditions for when the
Ramsey property for (the age of) $B$ is inherited by a semi-retraction $A
$ of $B$.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Mathias (Université de la Réunion)
DTSTART:20210210T134500Z
DTEND:20210210T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/5
DESCRIPTION:Title: Power-admissible sets and ill-founded omega-models\nby Ad
rian Mathias (Université de la Réunion) as part of Leeds Models and Sets
\n\n\nAbstract\nAbstract: In the 1960s admissible sets were introduced whi
ch are transitive sets modelling principles of $\\Sigma_1$ set-recursion.\
n\nIn 1971 Harvey Friedman introduced power-admissible sets\, which are tr
ansitive sets modelling principles of $\\Sigma_1^P$\, roughly $\\Sigma_1$
recursion in the power-set function.\n\nSeveral decades later I initiated
the study of provident sets\, which are transitive sets modelling principl
es of rudimentary recursion. Over the last fifty-odd years several workers
have found that ill-founded omega-models\, the axiom of constructibility
and techniques from proof theory bring unexpected insights into the struct
ure of these models of set-recursion.\n\nIn this talk I shall review these
results and the methods of proof.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erin Carmody (Fordham College)
DTSTART:20210217T164500Z
DTEND:20210217T180000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/6
DESCRIPTION:Title: The relationships between measurable and strongly compact car
dinals.(Part 1)\nby Erin Carmody (Fordham College) as part of Leeds Mo
dels and Sets\n\n\nAbstract\nThis talk is about the ongoing investigation
of the relationships between measurable and strongly compact cardinals. I
will present some of the history of the theorems in this theme\, includin
g Magidor's identity crisis\, and give new results. The theorems presente
d are in particular about the relationships between strongly compact cardi
nals and measurable cardinals of different Mitchell orders. One of the mai
n theorems is that there is a universe where $\\kappa_1$ and $\\kappa_2$ a
re the first and second strongly compact cardinals\, respectively\, and wh
ere $\\kappa_1$ is least with Mitchell order 1\, and $\\kappa_2$ is the le
ast with Mitchell order 2. Another main theorem is that there is a univer
se where $\\kappa_1$ and $\\kappa_2$ are the first and second strongly com
pact cardinals\, respectively\, with $\\kappa_1$ the least measurable card
inal such that $o(\\kappa_1) = 2$ and $\\kappa_2$ the least measurable car
dinal above $\\kappa_1$. This is a joint work in progress with Victoria G
itman and Arthur Apter.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erin Carmody (Fordham College)
DTSTART:20210224T164500Z
DTEND:20210224T180000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/7
DESCRIPTION:Title: The relationships between measurable and strongly compact car
dinals.(Part 2)\nby Erin Carmody (Fordham College) as part of Leeds Mo
dels and Sets\n\n\nAbstract\nThis talk is about the ongoing investigation
of the relationships between measurable and strongly compact cardinals. I
will present some of the history of the theorems in this theme\, includin
g Magidor's identity crisis\, and give new results. The theorems presente
d are in particular about the relationships between strongly compact cardi
nals and measurable cardinals of different Mitchell orders. One of the mai
n theorems is that there is a universe where $\\kappa_1$ and $\\kappa_2$ a
re the first and second strongly compact cardinals\, respectively\, and wh
ere $\\kappa_1$ is least with Mitchell order 1\, and $\\kappa_2$ is the le
ast with Mitchell order 2. Another main theorem is that there is a univer
se where $\\kappa_1$ and $\\kappa_2$ are the first and second strongly com
pact cardinals\, respectively\, with $\\kappa_1$ the least measurable card
inal such that $o(\\kappa_1) = 2$ and $\\kappa_2$ the least measurable car
dinal above $\\kappa_1$. This is a joint work in progress with Victoria G
itman and Arthur Apter.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dana Bartošová (University of Florida)
DTSTART:20210310T134500Z
DTEND:20210310T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/8
DESCRIPTION:Title: Universal minimal flows of group extensions\nby Dana Bart
ošová (University of Florida) as part of Leeds Models and Sets\n\n\nAbst
ract\nMinimal flows of a topological group G are often described as the bu
ilding blocks of dynamical systems with the acting group G. The universal
minimal flow is the most complicated one\, in the sense that it is minimal
and admits a homomorphism onto any minimal flow. We will study how group
extensions interact with universal minimal flows\, in particular extension
s of and by a compact group.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sonia Navarro Flores (Universidad Nacional Autónoma de México)
DTSTART:20210317T144500Z
DTEND:20210317T160000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/9
DESCRIPTION:Title: Ramsey spaces and Borel ideals\nby Sonia Navarro Flores (
Universidad Nacional Autónoma de México) as part of Leeds Models and Set
s\n\n\nAbstract\nIt is known that the Ellentuck space\, which is forcing e
quivalent to the Boolean algebra P(\\omega)/Fin forces a selective ultrafi
lter. The Ellentuck space is the prototypical example of a Ramsey space. T
he connection between Ramsey spaces\, ultrafilters\, and ideals has been e
xplored in different ways. Ramsey spaces theory has shown to be crucial t
o investigate Tukey order\, Karetov order\, and combinatorial properties.
This is why we investigate which ideals are related to a Ramsey space in t
he same sense that the ideal Fin is related to the Ellentuck space. In thi
s talk\, we present some results obtained.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Barbina (The Open University)
DTSTART:20210324T134500Z
DTEND:20210324T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/10
DESCRIPTION:Title: Model theory of Steiner triple systems\nby Silvia Barbin
a (The Open University) as part of Leeds Models and Sets\n\n\nAbstract\nA
Steiner triple system (STS) is a set together with a collection B of subse
ts of size 3 such that any two elements of the set belong to exactly one s
ubset in B. Finite STSs are well known combinatorial objects for which the
literature is extensive. Far fewer results have been obtained on their in
finite counterparts\, which are natural candidates for model-theoretic inv
estigation. I shall review some constructions of infinite STSs\, including
the Fraïssé limit of the class of finite STSs. I will then give an axio
matisation of the theory of the Fraïssé limit and describe some of its p
roperties. This is joint work with Enrique Casanovas.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marlene Koelbing (Universität Wien)
DTSTART:20210303T134500Z
DTEND:20210303T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/11
DESCRIPTION:Title: Distributivity spectrum of forcing notions\nby Marlene K
oelbing (Universität Wien) as part of Leeds Models and Sets\n\n\nAbstract
\nIn my talk\, I will introduce two different notions of a spectrum of dis
tributivity of forcings.\n \nThe first one is the fresh function spectrum\
, which is the set of regular cardinals lambda\, such that the forcing add
s a new function with domain lambda all whose initial segments are in the
ground model. I will provide several examples as well as general facts how
to compute the fresh function spectrum\, also discussing what sets are re
alizable as a fresh function spectrum of a forcing.\n \nThe second notion
is the combinatorial distributivity spectrum\, which is the set of possibl
e regular heights of refining systems of maximal antichains without common
refinement. We discuss the relation between the fresh function spectrum a
nd the combinatorial distributivity spectrum. We consider the special case
of P(omega)/fin (for which h is the minimum of the spectrum)\, and use a
forcing construction to show that it is consistent that the combinatorial
distributivity spectrum of P(omega)/fin contains more than one element.\n
\nThis is joint work with Vera Fischer and Wolfgang Wohofsky.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Falque (Université Paris-Sud)
DTSTART:20210428T144500Z
DTEND:20210428T160000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/12
DESCRIPTION:Title: Classification of oligomorphic groups with polynomial profil
es\, conjectures of Cameron and Macpherson.\nby Justine Falque (Univer
sité Paris-Sud) as part of Leeds Models and Sets\n\n\nAbstract\nLet G be
a group of permutations of a denumerable set E. The profile of G is the fu
nction f which counts\, for each n\, the (possibly infinite) number f(n) o
f orbits of G acting on the n-subsets of E. When f takes only finite value
s\, G is called oligomorphic.\n\n\nCounting functions arising this way\, a
nd their associated generating series\, form a rich yet apparently strongl
y constrained class. In particular\, Cameron conjectured in the late seven
ties that\, whenever the profile f(n) is bounded by a polynomial (we say t
hat G is P-oligomorphic)\, it is asymptotically equivalent to a polynomial
. In 1985\, Macpherson further asked whether the orbit algebra of G (a gra
ded commutative algebra invented by Cameron and whose Hilbert function is
f) was finitely generated.\n\n\nAfter providing some context and definitio
ns of the involved objects\, this talk will outline the proof of a classif
ication result of all (closed) P-oligomorphic groups\, of which the conjec
tures of Cameron and Macpherson are corollaries. The proof exploits classi
cal notions from group theory (notably block systems and their lattice pro
perties)\, commutative algebra\, and invariant theory. This research was a
joint work with Nicolas Thiéry.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Dobrinen (University of Denver)
DTSTART:20210505T164500Z
DTEND:20210505T180000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/13
DESCRIPTION:Title: Ramsey theory on infinite structures\nby Natasha Dobrine
n (University of Denver) as part of Leeds Models and Sets\n\n\nAbstract\nT
he Infinite Ramsey Theorem says that for any positive integer n\, given a
coloring of all n-element subsets of the natural numbers into finitely man
y colors\, there is an infinite set M of natural numbers such that all n-e
lement subsets of M have the same color. Infinite Structural Ramsey Theor
y is concerned with finding analogues of the Infinite Ramsey Theorem for F
raisse limits\, and also more generally for universal structures. In most
cases\, the exact analogue of Ramsey’s Theorem fails. However\, someti
mes one can find bounds of the following sort: Given a finite substructur
e A of an infinite structure S\, we let T(A\,S) denote the least number\,
if it exists\, such that for any coloring of the copies of A in S into fin
itely many colors\, there is a substructure S’ of S\, isomorphic to S\,
such that the copies of A in S’ take no more than T(A\,S) colors. If fo
r each finite substructure A of S\, this number T(A\,S) exists\, then we s
ay that S has “finite big Ramsey degrees”.\n\nIn the past six years\,
there has been a resurgence of investigations into the existence and chara
cterization of big Ramsey degrees for infinite structures\, leading to man
y new and exciting results and methods. We will present an overview of th
e area and some highlights of recent work by various author combinations f
rom among Balko\, Barbosa\, Chodounsky\, Coulson\, Dobrinen\, Hubicka\, Ko
njecny\, Masulovic\, Nesetril\, Patel\, Vena\, and Zucker.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ibrahim Mohammed (University of Leeds)
DTSTART:20210512T134500Z
DTEND:20210512T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/14
DESCRIPTION:Title: Hyperlogarithmic contraction groups\nby Ibrahim Mohammed
(University of Leeds) as part of Leeds Models and Sets\n\n\nAbstract\nCon
traction groups are a model theoretic structure introduced by F.V Kuhlmann
to help generalise the global behaviour of the logarithmic function on a
non-archimedean field. They consist of an ordered abelian group augmented
with a map called the contraction which collapses entire archimedean class
es to a single point. Kuhlmann proved in his paper that the theory of a pa
rticular type of contraction group had quantifier elimination and was weak
ly o-minimal (so every definable set is the finite union of convex sets an
d points).\n\nWe can go further and ask how a hyperlogarithmic function be
haves globally on a non-archimedean field. A hyper logarithm is the invers
e of a trans exponential\, which is any function that grows faster than al
l powers of exp. From an appropriate field equipped with a hyperlogarithm\
, we get a new type of structure with two contraction maps\, which we will
call 'Hyperlogarithmic contraction groups'. In this talk I will show how
the proof for Q.E and weak o-minimality given by Kuhlmann can be adapted t
o show that Hyperlogrithmic contraction groups also have these properties.
\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorottya Sziráki (Alfréd Rényi Institute of Mathematics)
DTSTART:20210519T134500Z
DTEND:20210519T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/15
DESCRIPTION:Title: The open dihypergraph dichotomy and the Hurewicz dichotomy f
or generalized Baire spaces\nby Dorottya Sziráki (Alfréd Rényi Inst
itute of Mathematics) as part of Leeds Models and Sets\n\n\nAbstract\nGene
ralized descriptive set theory studies analogues\, associated to uncountab
le regular cardinals $\\kappa$\, of well known topological spaces such as
the real line\, the Cantor space and the Baire space. A canonical example
is the generalized Baire space ${}^\\kappa\\kappa$ of functions $f:\\kappa
\\to\\kappa$ equipped with the ${<}\\kappa$-support topology. The open gra
ph dichotomy for a given set $X$ of reals is a strengthening of the perfec
t set property for $X$\, and it can also be viewed as the definable versio
n of the open coloring axiom restricted to $X$. Rapha\\"el Carroy\, Benjam
in Miller and D\\'aniel Soukup have recently introduced an $\\aleph_0$-dim
ensional generalization of the open graph dichotomy which implies several
well-known dichotomy theorems for Polish spaces.\n\nWe show that in Solova
y's model\, this $\\aleph_0$-dimensional open dihypergraph dichotomy holds
for all sets of reals. In our main theorem\, we obtain a version of this
previous result for generalized Baire spaces ${}^\\kappa\\kappa$ for uncou
ntable regular cardinals $\\kappa$. As an application\, we derive several
versions of the Hurewicz dichotomy for definable subsets of ${}^\\kappa\\k
appa$. This is joint work with Philipp Schlicht.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nam Trang (University of California\, Irvine)
DTSTART:20210526T164500Z
DTEND:20210526T180000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/16
DESCRIPTION:Title: Sealing of the Universally Baire sets\nby Nam Trang (Uni
versity of California\, Irvine) as part of Leeds Models and Sets\n\n\nAbst
ract\nA set of reals is universally Baire if all of its continuous preimag
es in topological spaces have the Baire property. Sealing is a type of gen
eric absoluteness\ncondition introduced by H. W. Woodin that asserts in st
rong terms that the theory of\nthe universally Baire sets cannot be change
d by set forcings. The Largest Suslin Axiom (LSA) is a determinacy axiom i
solated by Woodin. It as-\nserts that the largest Suslin cardinal is inacc
essible for ordinal definable bijections. \nLSA-over-uB is the statement t
hat in all (set) generic extensions there is a model of\nLSA whose Suslin\
, co-Suslin sets are the universally Baire sets.\n\nThe main result connec
ting these notions is: over some mild large cardinal theory\,\nSealing is
equiconsistent with LSA-over-uB. As a consequence\, we obtain that\nSealin
g is weaker than the theory “ZFC+there is a Woodin cardinal which is a l
imit\nof Woodin cardinals”. This significantly improves upon the earlier
consistency proof\nof Sealing by Woodin and shows that Sealing is not a s
trong consequence of\nsupercompactness as suggested by Woodin’s result.\
n\nWe discuss some history that leads up to these results as well as the r
ole these\nnotions and results play in recent developments in descriptive
inner model theory\, an\nemerging field in set theory that explores deep c
onnections between descriptive set\ntheory\, in particular\, the study of
canonical models of determinacy and its HOD\, and\ninner model theory\, th
e study of canonical inner models of large cardinals. Time permitted\, we
will sketch proofs of some of the results.\n\nThis talk is based on joint
work with G. Sargsyan.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jing Zhang (Bar-Ilan University)
DTSTART:20210602T134500Z
DTEND:20210602T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/17
DESCRIPTION:Title: When does compactness imply guessing?\nby Jing Zhang (Ba
r-Ilan University) as part of Leeds Models and Sets\n\n\nAbstract\nLarge c
ardinal properties\, or more generally compactness principles\, usually gi
ve rise to certain guessing principles. For example\, if kappa is measurab
le\, then the diamond principle at kappa holds and if kappa is supercompac
t\, then the Laver diamond principle holds. It is a long-standing open que
stion whether weak compactness is consistent with the failure of diamond.
In the 80’s\, Woodin showed it is consistent that diamond fails at a gre
atly Mahlo cardinal\, based on the analysis on Radin forcing. It turns out
that this method cannot yield significant improvement to Woodin’s resul
t. In particular\, we show that in any Radin forcing extension with respec
t to a measure sequence on kappa\, if kappa is weakly compact\, then the d
iamond principle at kappa holds. Despite the negative result\, there are s
till some positive results obtained by refining the analysis of Radin forc
ing\, demonstrating that diamond can fail at a strongly inaccessible cardi
nal satisfying strong compactness properties. Joint work with Omer Ben-Ner
ia.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vahagn Aslanyan (University of East Anglia)
DTSTART:20210609T134500Z
DTEND:20210609T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/18
DESCRIPTION:Title: A geometric approach to some systems of exponential equation
s\nby Vahagn Aslanyan (University of East Anglia) as part of Leeds Mod
els and Sets\n\n\nAbstract\nI will discuss three important conjectures on
complex exponentiation\, namely\, Schanuel’s conjecture\, Zilber’s Exp
onential Algebraic Closedness (EAC) conjecture and Zilber’s quasiminimal
ity conjecture\, and explain how those conjectures are related to each oth
er and to the model theory of complex exponentiation. I will mainly focus
on the EAC conjecture which states that certain systems of exponential equ
ations have complex solutions. Then I will show how it can be verified for
systems of exponential equations with dominant additive projection for ab
elian varieties. All the necessary concepts related to abelian varieties w
ill be defined in the talk. The analogous problem for algebraic tori (i.e.
for usual complex exponentiation) was solved earlier by Brownawell and Ma
sser. If time permits\, I will show how our method can be used to give a n
ew proof of their result. This is joint work with Jonathan Kirby and Vince
nzo Mantova.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvy Anscombe (Institut de Mathématiques de Jussieu-Paris Rive G
auche)
DTSTART:20210616T134500Z
DTEND:20210616T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/19
DESCRIPTION:Title: Some existential theories of fields\nby Sylvy Anscombe (
Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of Leeds
Models and Sets\n\n\nAbstract\nBuilding on previous work\, I will discuss
Turing reductions between various fragments of theories of fields. In part
icular\, we exhibit several theories of fields Turing equivalent to the ex
istential theory of the rational numbers. This is joint work with Arno Feh
m.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhe (Vincent) Ye (Institut de Mathématiques de Jussieu-Paris Ri
ve Gauche)
DTSTART:20210623T124500Z
DTEND:20210623T140000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/20
DESCRIPTION:Title: The étale open topology and the stable fields conjecture\nby Jinhe (Vincent) Ye (Institut de Mathématiques de Jussieu-Paris Rive
Gauche) as part of Leeds Models and Sets\n\n\nAbstract\nFor any field $K$
\, we introduce natural topologies on $K$-points of varieties over $K$\, w
hich is defined to be the weakest topology such that étale morphisms are
open. This topology turns out to be natural in a lot of settings. For exam
ple\, when $K$ is algebraically closed\, it is easy to see that we have th
e Zariski topology\, and the procedure picks up the valuation topology in
many henselian valued fields. Moreover\, many topological properties corre
spond to the algebraic properties of the field. As an application of this
correspondence\, we will show that large stable fields are separably close
d. Joint work with Will Johnson\, Chieu-Minh Tran\, and Erik Walsberg.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Adam-Day (University of Oxford)
DTSTART:20211013T124500Z
DTEND:20211013T140000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/21
DESCRIPTION:Title: Rigid branchwise-real tree orders\nby Sam Adam-Day (Univ
ersity of Oxford) as part of Leeds Models and Sets\n\n\nAbstract\nA branch
wise-real tree order is a partial order tree in which every branch is isom
orphic to a real interval. In this talk\, I give several methods of constr
ucting examples of these which are rigid (i.e. without non-trivial automor
phisms)\, subject to increasing uniformity conditions. I show that there i
s a rigid branchwise-real tree order in which every branching point has th
e same degree\, one in which every point is branching and of the same degr
ee\, and finally one in which every point is branching of the same degree
and which admits no monotonic function into the reals. Trees are grown ite
ratively in stages\, and a key technique is the construction (in ZFC) of a
family of colourings of (0\,infty) which is 'sufficiently generic'\, usin
g these colourings to determine how to proceed with the construction.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirna Džamonja (CNRS – Université de Paris)
DTSTART:20211020T124500Z
DTEND:20211020T140000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/22
DESCRIPTION:Title: On the universality problem for $\\aleph_2$-Aronszajn and wi
de $\\aleph_2$ Aronszajn trees\nby Mirna Džamonja (CNRS – Universit
é de Paris) as part of Leeds Models and Sets\n\n\nAbstract\nWe report on
a joint work in progress with Rahman Mohammadpour in which we study the pr
oblem of the possible existence of a universal tree under weak embeddings
in the classes of $\\aleph_2$-Aronszajn and wide $\\aleph_2$-Aronszajn tre
es. This problem is more complex than previously thought\, in particular i
t seems not to be resolved under ShFA + CH using the technology of weakly
Lipshitz trees. We show that under CH\, for a given $\\aleph_2$-Aronszajn
tree T without a weak ascent path\, there is an $\\aleph_2$-cc countably c
losed forcing forcing which specialises T and adds an $\\aleph_2$-Aronszaj
n tree which does not embed into T. One cannot however apply the ShFA to t
his forcing.\n\nFurther\, we construct a model à la Laver-Shelah in which
there are $\\aleph_2$-Aronszajn trees\, but none is universal. Work in pr
ogress is to obtain an analogue for universal wide $\\aleph_2$-Aronszajn t
rees. We also comment on some negative ZFC results in the case that the em
beddings are assumed to have a strong preservation property.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilip Raghavan (National University of Singapore)
DTSTART:20211027T144500Z
DTEND:20211027T160000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/23
DESCRIPTION:Title: Galvin’s problem in higher dimensions\nby Dilip Raghav
an (National University of Singapore) as part of Leeds Models and Sets\n\n
\nAbstract\nThis talk will discuss recent work on Galvin's conjecture in R
amsey theory. I will review the background and discuss previous work on th
e two dimensional case before focusing on the recent work on dimensions gr
eater than 2. This is joint work with Stevo Todorcevic.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katrin Tent (Westfälische Wilhelms-Universität Münster)
DTSTART:20211103T134500Z
DTEND:20211103T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/24
DESCRIPTION:by Katrin Tent (Westfälische Wilhelms-Universität Münster)
as part of Leeds Models and Sets\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Gitman (CUNY Graduate Center)
DTSTART:20211110T134500Z
DTEND:20211110T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/25
DESCRIPTION:Title: Set theory without powerset\nby Victoria Gitman (CUNY Gr
aduate Center) as part of Leeds Models and Sets\n\n\nAbstract\nMany natura
l set-theoretic structures satisfy the basic axioms of set theory\, but no
t the powerset axiom. These include the collections $H_{\\kappa^+}$ of set
s whose transitive closure has size at most $\\kappa$\, forcing extensions
of models of ${\\rm ZFC}$ by pretame (but not tame) forcing\, and first-o
rder models that are morally equivalent to models of the second-order Kell
ey-Morse set theory (with class choice). It turns out that a reasonable se
t theory in the absence of the powerset axiom is not simply ${\\rm ZFC}$ w
ith the powerset axiom removed. Without the powerset axiom\, the Replaceme
nt scheme is not equivalent to the Collection scheme\, and the various for
ms of the Axiom of Choice are not equivalent. In this talk\, I will give a
n overview of the properties of a robust set theory without powerset\, ${\
\rm ZFC}^-$\, whose axioms are ${\\rm ZFC}$ without the powerset axiom\, w
ith the Collection scheme instead of the Replacement scheme and the Well-O
rdering Principle instead of the Axiom of Choice. While a great deal of st
andard set theory can be carried out in ${\\rm ZFC}^-$\, for instance\, fo
rcing works mostly as it does in ${\\rm ZFC}$\, there are several importan
t properties that are known to fail and some which we still don't know whe
ther they hold. For example\, the Intermediate Model Theorem fails for ${\
\rm ZFC}^-$\, and so does ground model definability\, and it is not known
whether ${\\rm HOD}$ is definable. I will also discuss a strengthening of
${\\rm ZFC}^-$ obtained by adding the Dependent Choice Scheme\, and some r
ather strange ${\\rm ZFC}^-$-models.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica VanDieren (Robert Morris University)
DTSTART:20211117T134500Z
DTEND:20211117T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/26
DESCRIPTION:Title: Twenty Years of Tameness\nby Monica VanDieren (Robert Mo
rris University) as part of Leeds Models and Sets\n\n\nAbstract\nIn the 19
70s Saharon Shelah initiated a program to develop classification theory fo
r non-elementary classes\, and eventually settled on the setting of abstra
ct elementary classes. For over three decades\, limited progress was made
\, most of which required additional set theoretic axioms. In 2001\, Rami
Grossberg and I introduced the model theoretic concept of tameness which o
pened the door for stability results in abstract elementary classes in ZFC
. During the following 20 years\, tameness along with limit models have b
een used by several mathematicians to prove categoricity theorems and to d
evelop non-first order analogs to forking calculus and stability theory\,
solving a very large number of problems posed by Shelah in ZFC. Recently\,
Marcus Mazari-Armida found applications to Abelian group theory and ring
theory. In this presentation I will highlight some of the more surprising
results involving tameness and limit models.\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noa Lavi (Politecnico di Torino)
DTSTART:20211125T134500Z
DTEND:20211125T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/27
DESCRIPTION:by Noa Lavi (Politecnico di Torino) as part of Leeds Models an
d Sets\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Postponed to 15th December due to strike action
DTSTART:20211201T134500Z
DTEND:20211201T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/28
DESCRIPTION:by Postponed to 15th December due to strike action as part of
Leeds Models and Sets\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anush Tserunyan (McGill University)
DTSTART:20211208T134500Z
DTEND:20211208T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/29
DESCRIPTION:by Anush Tserunyan (McGill University) as part of Leeds Models
and Sets\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aris Papadopoulos (University of Leeds)
DTSTART:20211215T134500Z
DTEND:20211215T150000Z
DTSTAMP:20260404T095242Z
UID:ModelsandSets/30
DESCRIPTION:Title: Around Generalised Indiscernibles and Higher-arity Independe
nce Properties\nby Aris Papadopoulos (University of Leeds) as part of
Leeds Models and Sets\n\n\nAbstract\nThe machinery of generalised indiscer
nibles has played a key role in recent developments of stability theory. O
ne of the most important applications of this machinery is characterising
dividing lines by collapsing indiscernibles\, a programme essentially trac
ing back to the early work of Shelah in the 1980s which has seen a resurge
nce lately\, starting with the work of Scow.\nIn my talk\, I will survey t
he main definitions and some important notions concerning these generalise
d indiscernibles and give some examples of characterising dividing lines b
y collapsing indiscernibles. Finally\, if time permits\, I will discuss an
application of generalised indiscernibles to higher-arity independence pr
operties\, showing that IP_k can be witnessed by formulas in singleton var
iables if one allows parameters (from some model).\n
LOCATION:https://stable.researchseminars.org/talk/ModelsandSets/30/
END:VEVENT
END:VCALENDAR