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2 2019

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One Henkin Quantifier in the Empty Vocabulary Suffices for Undecidability

Zdanowski Konrad

Fundamenta Informaticae

2019

Vol. 164, nr 4

375--386

We prove that there are single Henkin quantifiers such that first order logic augmented by one of these quantifiers is undecidable in the empty vocabulary. We estimate the size of such quantifiers proving undecidability of Lø(H12) and Lø(E10).

A Modal Logic of a Truth Definition for Finite Models

Czarnecki Marek, Zdanowski Konrad

Fundamenta Informaticae

2019

Vol. 164, nr 4

299--325

The property of being true in almost all finite, initial segments of the standard model of arithmetic is ∑02 –complete. Thus, it admits a kind of a truth definition. We define such an arithmetical predicate. Then, we define its modal logic SL and prove a completeness theorem with respect to finite models semantics. The proof that SL is the modal logic of the approximate truth definition for finite arithmetical models is based on an extension of SL by a fixed-point construction.