9 citations · 36 across the 29 of their papers we have counts for
30 papers
Fixed points in abstract provability structures
Tsubasa Kumasaka, Taishi Kurahashi
We study fixed points in abstract provability structures (APSs), which were introduced by Beklemishev and Shamkanov as an order-theoretic framework for studying Gödel's second inco…
On collection schemes and Gaifman's splitting theorem
Taishi Kurahashi, Yoshiaki Minami
We study model theoretic characterizations of various collection schemes over from the viewpoint of Gaifman's splitting theorem. Among other things, we prove that f…
Interpolation properties for the bimodal provability logic
Haruka Kogure, Taishi Kurahashi
We study interpolation properties for Shavrukov's bimodal logic of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic $\mathbf{GR}…
The Modal Logic of Provability and Forcing
Taishi Kurahashi, Rihito Takase
Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic . Hamkins and Löwe studied the modal logical aspe…
Cut-free sequent calculi for the provability logic D
Ryo Kashima, Taishi Kurahashi, Sohei Iwata +1
We say that a Kripke model is a GL-model if the accessibility relation is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by…
Pour-El's Landscape
Taishi Kurahashi, Albert Visser
We study the effective versions of several notions related to incompleteness, undecidability and inseparability along the lines of Pour-El's insights. Firstly, we strengthen Pour-E…
Certified -sentences
Taishi Kurahashi, Albert Visser
In this paper, we study the employment of -sentences with certificates, i.e., -sentences where a number of principles is added to ensure that the witness is sufficiently…
On the conservation results for local reflection principles
Haruka Kogure, Taishi Kurahashi
For a class of formulas, local reflection principle for a theory of arithmetic is a scheme formalizing the -soundness of . Beklemishev proved…
The finite frame property of some extensions of the pure logic of necessitation
Taishi Kurahashi, Yuta Sato
We study the finite frame property of some extensions of Fitting, Marek, and Truszczyński's pure logic of necessitation . For any natural numbers , we introduce t…
Prenex normalization and the hierarchical classification of formulas
Makoto Fujiwara, Taishi Kurahashi
Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give…
Visser frames for sublogics of
Yuya Okawa, Taishi Kurahashi
We study the modal completeness and the finite frame property of several sublogics of the logic of interpretability with respect to Visser frames, which are also call…
Incompleteness and undecidability of theories consistent with
Taishi Kurahashi
We prove the following version of the first incompleteness theorem that simultaneously strengthens Mostowski's theorem and Vaught's theorem: For any c.e. family $\{ T_i \}_{i \in ω…
Arithmetical completeness theorems for monotonic modal logics
Haruka Kogure, Taishi Kurahashi
We investigate modal logical aspects of provability predicates satisfying the following condition: : If , then $T \vdash \mathrm{Pr}…
The provability logic of all provability predicates
Taishi Kurahashi
We prove that the provability logic of all provability predicates is exactly Fitting, Marek, and Truszczyński's pure logic of necessitation . Moreover, we introduce thr…
The persistence principle over weak interpretability logic
Sohei Iwata, Taishi Kurahashi, Yuya Okawa
We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic…
Some observations on the FGH theorem
Taishi Kurahashi
We investigate the Friedman--Goldfarb--Harrington theorem from two perspectives. Firstly, in the frameworks of classical and modal propositional logics, we study the forms of sente…
Disjunction and existence properties in modal arithmetic
Taishi Kurahashi, Motoki Okuda
We systematically study several versions of the disjunction and the existence properties in modal arithmetic. First, we newly introduce three classes , ,…
Conservation theorems on semi-classical arithmetic
Makoto Fujiwara, Taishi Kurahashi
We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic and intuitionistic arithmetic $\math…
Topological semantics of conservativity and interpretability logics
Sohei Iwata, Taishi Kurahashi
We introduce and develop a topological semantics of conservativity logics and interpretability logics. We prove the topological compactness theorem of consistent normal extensions…
On inclusions between quantified provability logics
Taishi Kurahashi
We investigate several consequences of inclusion relations between quantified provability logics. Moreover, we give a necessary and sufficient condition for the inclusion relation…
Refining the arithmetical hierarchy of classical principles
Makoto Fujiwara, Taishi Kurahashi
We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly…
Prenex normal form theorems in semi-classical arithmetic
Makoto Fujiwara, Taishi Kurahashi
Akama et al. systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they fir…
The fixed point and the Craig interpolation properties for sublogics of
Sohei Iwata, Taishi Kurahashi, Yuya Okawa
We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic . We provide a complete description of these sublogi…
Modal completeness of sublogics of the interpretability logic
Taishi Kurahashi, Yuya Okawa
We study modal completeness and incompleteness of several sublogics of the interpretability logic . We introduce the sublogic , and prove that $\mathbf{…