#матлог #учёба #семинар #не_мехмат #ВШЭ

Уважаемые коллеги, приглашаем вас принять участие в заседании научного семинара "Современные проблемы математической логики" в ВШЭ.

Семинар пройдет в очном формате с одновременной трансляцией
на Математическом факультете ВШЭ, в аудитории 110 (ул. Усачева, д. 6). Мы будем транслировать доклад в zoom, но лучше приходите очно.
Если вам нужен пропуск в здание матфака, пришлите ваши ФИО и просьбу о пропуске на почту kudinov.andrey@gmail.com.

Дата и время: 20.02.2026 в 16:20

Язык доклада: английский.

Speaker: Sayantan Roy

Title: Abstract Model Structures and Compactness Theorems

Abstract: The compactness theorem for a logic states, roughly, that the satisfiability of a set of wffs can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the syntactic/semantic particularities of the corresponding logic. In this talk, using the notion of abstract model structures, we investigate a generalized notion of compactness that is independent of these. Thus, in terms of spirit, this work belongs to the subject known as abstract model theory although methodologically, it goes beyond it (e.g., we do not maintain the same commitment lack the strong commitment to the conventional concrete systems of logic that are characteristic features of works in this area). We also differ from a more categorical take to the subject since our approach is purely set-theoretic. We, however, do not compromise with the level of generality, and obtain several characterization theorems for a particular class of compact abstract model structures, generalizing the traditional Henkin-style, topological and ultrproduct proofs respectively. Finally, some open problems and directions for future research are discussed as well.

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