Universiteit van Amsterdam

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Institute for Logic, Language and Computation

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19 October 2016, Colloquium on Mathematical Logic, Fedor Pakhomov

Speaker: Fedor Pakhomov
Title: Transitive modal logics and second-order theories
Date: Wednesday 19 October 2016
Time: 16:00-17:00
Location: Zaal 012, Drift 23, Utrecht

Abstract: For Kripke semantics modal language could express properties that could not be expressed by first-order formulas. It were shown by S.K. Thomason that there is a certain kind of effective reduction of second-order logic to modal logic (with semantical consequence relation). We show that there is an effective reduction of second-order logic to S4 with nominals.
For every Kripke complete logic L its Kuznetsov index is the least cardinal \kappa such that every refutable formula of this logic is already refutable in an L-frame of the cardinality less than \kappa. A.V. Kuznetsov had raised a question of characterization of all Kuznetsov indexes for superintuitonistic logics and for extensions of S4. M.Kracht had proved a theorem that says that a cardinal \kappa is a Kuznetsov index of a Kripke complete modal logic iff it is a (likewise defined) index of some \Pi^1_1-theory with countable signature. From our reduction result we conclude that the analogue of Kracht theorem for extensions of S4 with nominals holds.

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