9 papers
Modal logics of conjunctively closed provability predicates
Haruka Kogure, Taishi Kurahashi
We investigate non-normal modal logics corresponding to provability predicates satisfying the derivability condition : $T\vdash\mathrm{Pr}_T(\ulcorne…
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…
Refinements of provability and consistency principles for the second incompleteness theorem
Taishi Kurahashi
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of t…
Hierarchical formula classes with respect to semi-classical prenex normalization
Makoto Fujiwara, Taishi Kurahashi
In [10], the authors formalized the standard transformation procedure for prenex normalization of first-order formulas and showed that the classes and …
Extensional Independence
Taishi Kurahashi, Albert Visser
Joel Hamkins asks whether there is a -formula such that is independent over , if this theory is consistent, where this construction is extensional…
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)…
Smullyan's truth and provability
Taishi Kurahashi, Kohei Tominaga
We revisit Smullyan's paper ``Truth and Provability'' (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan's frame…
Lyndon interpolation property for extensions of and intermediate propositional logics
Taishi Kurahashi
We study the Lyndon interpolation property (LIP) and the uniform Lyndon interpolation property (ULIP) for extensions of and intermediate propositional logics. We prov…