Takao Yuyama - Academia.edu (original) (raw)

Takao Yuyama

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Papers by Takao Yuyama

Research paper thumbnail of Groups Whose Word Problems Are Accepted by Abelian <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math></span><span class="katex-html" aria-hidden="true"></span></span>G$$-Automata

Lecture Notes in Computer Science, 2023

Research paper thumbnail of Term-Space Semantics of Typed Lambda Calculus

Notre Dame Journal of Formal Logic, 2020

Barendregt gave a sound semantics of the simple type assignment system λ→ by generalizing Tait’s ... more Barendregt gave a sound semantics of the simple type assignment system λ→ by generalizing Tait’s proof of the strong normalization theorem. In this paper, we aim to extend the semantics so that the completeness theorem holds.

Research paper thumbnail of On Hilbert’s tenth problem over subrings of Q

For a subring R of the rationals Q, Hilbert’s tenth problem over R, denoted by HTP(R), is the set... more For a subring R of the rationals Q, Hilbert’s tenth problem over R, denoted by HTP(R), is the set of multivariate polynomial equations with integer coefficients which has a solution in R. The undecidability status of HTP(Q) is a big open problem in both computability theory and number theory. Although it is possible that HTP(Q) has incomplete Turing degree, no attempt has been made so far to characterize the undecidability of HTP(Q). In this thesis, we introduce a new notion called HTP-nontriviality of a subring of Q, and show that the following conditions are equivalent: (1) HTP(Q) is undecidable, (2) there are nonmeager many HTP-nontrivial subrings of Q and (3) Player I has a winning strategy for the Banach-Mazur game for the set of HTP-nontrivial subrings. We also show a measure-theoretic analogue for this result.

Research paper thumbnail of Groups Whose Word Problems Are Accepted by Abelian <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math></span><span class="katex-html" aria-hidden="true"></span></span>G$$-Automata

Lecture Notes in Computer Science, 2023

Research paper thumbnail of Term-Space Semantics of Typed Lambda Calculus

Notre Dame Journal of Formal Logic, 2020

Barendregt gave a sound semantics of the simple type assignment system λ→ by generalizing Tait’s ... more Barendregt gave a sound semantics of the simple type assignment system λ→ by generalizing Tait’s proof of the strong normalization theorem. In this paper, we aim to extend the semantics so that the completeness theorem holds.

Research paper thumbnail of On Hilbert’s tenth problem over subrings of Q

For a subring R of the rationals Q, Hilbert’s tenth problem over R, denoted by HTP(R), is the set... more For a subring R of the rationals Q, Hilbert’s tenth problem over R, denoted by HTP(R), is the set of multivariate polynomial equations with integer coefficients which has a solution in R. The undecidability status of HTP(Q) is a big open problem in both computability theory and number theory. Although it is possible that HTP(Q) has incomplete Turing degree, no attempt has been made so far to characterize the undecidability of HTP(Q). In this thesis, we introduce a new notion called HTP-nontriviality of a subring of Q, and show that the following conditions are equivalent: (1) HTP(Q) is undecidable, (2) there are nonmeager many HTP-nontrivial subrings of Q and (3) Player I has a winning strategy for the Banach-Mazur game for the set of HTP-nontrivial subrings. We also show a measure-theoretic analogue for this result.

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