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Provability interpretation of non-normal modal logics having neighborhood semantics
Haruka Kogure
We study provability predicates satisfying the following condition from a modal logical perspective: if …
Modal logical aspects of provability predicates and consistency statements
Haruka Kogure, Taishi Kurahashi
This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the…
Doubly partially conservative sentences
Haruka Kogure, Taishi Kurahashi
The purpose of the present paper is to analyze several variants of Solovay's theorem on the existence of doubly partially conservative sentences. First, we investigate sentence…
A variety of partially conservative sentences
Haruka Kogure, Taishi Kurahashi
We study the existence of a sentence which is simultaneously -conservative over consistent RE extensions and of Peano Arithmetic for various reasonable pairs $(Γ, Θ)…