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Mathematical Logic Weekly Seminar
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سمینار هفتگی منطق ریاضی
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TITLE
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Universal Theories and Compactly Expandable Models
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SPEAKER
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Enrique Casanovas
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Universitat de Barcelona, Spain
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TIME
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Wednesday, December 16, 2020,
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16:30 - 18:30
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VENUE |
(Online)
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SUMMARY |
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Let M be structure of cardinality κ with language τ(M)≤κ. We say that is \textit{compactly expandable} if for every theory T of language τ(T) with τ(M)⊆τ(T) and |T|≤κ can be realised in an expansion of M, whenever every finite subset of T can be realised in an expansion of M. We say that M is \textit{expandable} if the requirement of finite satisfiability can be weakened to: T is consistent with the complete theory Th(M) of M. Clearly, expandable models are compactly
expandable. The existence of a compactly expandable model which is not expandable was conjectured in \cite{95} and has been recently proved in \cite{19} using the
notion of universal theory and the logic of the quantifier of cofinality ω. We plan to present these results.
References
[1] E. Casanovas. Compactly expandable models and stability. The Journal of
Symbolic Logic, 60:673–683, 1995.
[2] E. Casanovas and S. Shelah. Universal theories and compactly expandable
models. The Journal of Symbolic Logic, 84:1215–1223, 2019.
To join this webinar, please send an email to r.zoghi@gmail.com.
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تهران، ضلع جنوبی
ميدان شهيد باهنر (نياوران)، پژوهشگاه
دانشهای بنيادی، پژوهشکده رياضيات
School of
Mathematics, Institute for Research in
Fundamental Sciences (IPM), Niavaran
Bldg., Niavaran Square, Tehran
ipmmath@ipm.ir
♦ +98 21
22290928 ♦
math.ipm.ir |
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