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BEGIN:VEVENT
SUMMARY:Victoria Gitman (City University of New York)
DTSTART:20200506T150000Z
DTEND:20200506T163000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/1/">Elementary embeddings and smaller large cardinals</a>\nby
  Victoria Gitman (City University of New York) as part of Oxford Set Theor
 y Seminar\n\nLecture held in Online\, via Zoom.\n\nAbstract\nA common them
 e in the definitions of larger large cardinals is the existence of element
 ary embeddings from the universe into an inner model. In contrast\, smalle
 r large cardinals\, such as weakly compact and Ramsey cardinals\, are usua
 lly characterized by their combinatorial properties such as existence of l
 arge homogeneous sets for colorings. It turns out that many familiar small
 er large cardinals have elegant elementary embedding characterizations. Th
 e embeddings here are correspondingly 'small'\;&nbsp\;they are between tra
 nsitive set models of set theory\, usually the size of the large cardinal 
 in question. The study of these elementary embeddings has led us to isolat
 e certain important properties via which we have defined robust hierarchie
 s of large cardinals below a measurable cardinal. In this talk\, I will in
 troduce these types of elementary embeddings and discuss the large cardina
 l hierarchies that have come out of the analysis of their properties. The 
 more recent results in this area are a joint work with Philipp Schlicht.\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel David Hamkins (Oxford University)
DTSTART:20200520T150000Z
DTEND:20200520T163000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/2/">Bi-interpretation of weak set theories</a>\nby Joel David
  Hamkins (Oxford University) as part of Oxford Set Theory Seminar\n\n\nAbs
 tract\nSet theory exhibits a truly robust mutual interpretability phenomen
 on: in any model of one set theory we can define models of diverse other s
 et theories and vice versa. In any model of ZFC\, we can define models of 
 ZFC + GCH and also of ZFC + ¬CH and so on in hundreds of cases. And yet\,
  it turns out\, in no instance do these mutual interpretations rise to the
  level of bi-interpretation. Ali Enayat proved that distinct theories exte
 nding ZF are never bi-interpretable\, and models of ZF are bi-interpretabl
 e only when they are isomorphic. So there is no nontrivial bi-interpretati
 on phenomenon in set theory at the level of ZF or above.&nbsp\; Neverthele
 ss\, for natural weaker set theories\, we prove\, including ZFC- without p
 ower set and Zermelo set theory Z\, there are nontrivial instances of bi-i
 nterpretation. Specifically\, there are well-founded models of ZFC- that a
 re bi-interpretable\, but not isomorphic---even $\\langle H_{\\omega_1}\,\
 \in\\rangle$ and $\\langle H_{\\omega_2}\,\\in\\rangle$ can be bi-interpre
 table---and there are distinct bi-interpretable theories extending ZFC-. S
 imilarly\, using a construction of Mathias\, we prove that every model of 
 ZF is bi-interpretable with a model of Zermelo set theory in which the rep
 lacement axiom fails. This is joint work with Alfredo Roque Freire.\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Enayat (Gothenberg)
DTSTART:20200527T150000Z
DTEND:20200527T163000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/3/">Leibnizian and anti-Leibnizian motifs in set theory</a>\n
 by Ali Enayat (Gothenberg) as part of Oxford Set Theory Seminar\n\n\nAbstr
 act\nLeibniz's principle of identity of indiscernibles at first sight appe
 ars completely&nbsp\;unrelated to set theory\, but Mycielski (1995) formul
 ated a set-theoretic axiom&nbsp\;nowadays referred to as LM (for Leibniz-M
 ycielski) which captures the spirit of Leibniz's dictum in the&nbsp\;follo
 wing sense:&nbsp\; LM holds in a model M of ZF iff M is elementarily&nbsp\
 ;equivalent to a model M* in which there is no pair of indiscernibles.&nbs
 p\; LM was further investigated in a 2004&nbsp\; paper of mine\, which inc
 ludes a proof that LM is equivalent to the global form of the Kinna-Wagner
  selection principle in set theory.&nbsp\; On the other hand\, one can for
 mulate a strong negation of Leibniz's principle by first adding a unary pr
 edicate I(x) to the usual language of set theory\, and then augmenting ZF 
 with a scheme that ensures that I(x) describes a proper class of indiscern
 ibles\, thus giving rise to an extension ZFI of ZF that I showed (2005) to
  be intimately related to Mahlo cardinals of finite order. In this talk I 
 will give an expository account of the above and related results that atte
 st to a lively interaction between set theory and Leibniz's principle of i
 dentity of indiscernibles.\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Bacal Switzer (City University of New York)
DTSTART:20200617T150000Z
DTEND:20200617T163000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/4/">Some Set Theory of Kaufmann Models</a>\nby Corey Bacal Sw
 itzer (City University of New York) as part of Oxford Set Theory Seminar\n
 \n\nAbstract\nA Kaufmann model is an $\\omega_1$-like\, recursively satura
 ted\, rather classless model of PA. Such models were shown to exist by Kau
 fmann under the assumption that $\\diamondsuit$ holds\, and in ZFC by Shel
 ah via an absoluteness argument involving strong logics. They are importan
 t in the theory of models of arithmetic notably because they show that man
 y classic results about countable\, recursively saturated models of arithm
 etic cannot be extended to uncountable models. They are also a particularl
 y interesting example of set theoretic incompactness at $\\omega_1$\, simi
 lar to an Aronszajn tree.</p>\n\n<p>\nIn this talk we’ll look at several
  set theoretic issues relating to this class of models motivated by the se
 emingly naïve question of whether or not such models can be killed by for
 cing without collapsing $\\omega_1$. Surprisingly the answer to this quest
 ion turns out to be independent: under $\\mathsf{MA}_{\\aleph_1}$ no $\\om
 ega_1$-preserving forcing can destroy Kaufmann-ness whereas under $\\diamo
 ndsuit$ there is a Kaufmann model $M$ and a Souslin tree $S$ so that forci
 ng with $S$ adds a satisfaction class to $M$ (thus killing rather classles
 sness). The techniques involved in these proofs also yield another surpris
 ing side of Kaufmann models: it is independent of ZFC whether the class of
  Kaufmann models can be axiomatized in the logic $L_{\\omega_1\, \\omega}(
 Q)$ where $Q$ is the quantifier “there exists uncountably many”. This 
 is the logic used in Shelah’s aforementioned result\, hence the interest
  in this level of expressive power.\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Blass (University of Michigan)
DTSTART:20201021T150000Z
DTEND:20201021T163000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/5
DESCRIPTION:by Andreas Blass (University of Michigan) as part of Oxford Se
 t Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirna Džamonja (INSTITUT FOR HISTORY AND PHILOSOPHY OF SCIENCES A
 ND TECHNIQUES\, CNRS & UNIVERSITÉ PANTHÉON SORBONNE\, PARIS AND INSTITUT
 E OF MATHEMATICS\, CZECH ACADEMY OF SCIENCES\, PRAGUE)
DTSTART:20201104T160000Z
DTEND:20201104T173000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/6/">On wide Aronszajn trees</a>\nby Mirna Džamonja (INSTITUT
  FOR HISTORY AND PHILOSOPHY OF SCIENCES AND TECHNIQUES\, CNRS & UNIVERSIT
 É PANTHÉON SORBONNE\, PARIS AND INSTITUTE OF MATHEMATICS\, CZECH ACADEMY
  OF SCIENCES\, PRAGUE) as part of Oxford Set Theory Seminar\n\nAbstract: T
 BA\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Goldberg (Harvard University)
DTSTART:20201118T160000Z
DTEND:20201118T173000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/7/">Even ordinals and the Kunen inconsistency</a>\nby Gabriel
  Goldberg (Harvard University) as part of Oxford Set Theory Seminar\n\nAbs
 tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kameryn J Williams (UNIVERSITY OF HAWAI’I AT MĀNOA)
DTSTART:20201202T160000Z
DTEND:20201202T173000Z
DTSTAMP:20260404T111445Z
UID:oxford-set-theory/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/oxfor
 d-set-theory/8/">The geology of inner mantles</a>\nby Kameryn J Williams (
 UNIVERSITY OF HAWAI’I AT MĀNOA) as part of Oxford Set Theory Seminar\n\
 nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/oxford-set-theory/8/
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