Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Toshiyasu Arai"'
The Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. It is normally held every three years and rotates among countries in the Asia-Pacific region. The 11th Asian Logic Conference was held at the Nati
Autor:
Chi Tat Chong, Rodney G Downey, Qi Feng, Hirotaka Kikyo, Hiroakira Ono, Toshiyasu Arai, Jorg Brendle
The 10th Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. This meeting is held every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, inc
Publikováno v:
The Bulletin of Symbolic Logic. 27:168-186
Following our [6], though with somewhat different methods here, further variants of Goodstein sequences are introduced in terms of parameterized Ackermann–Péter functions. Each of the sequences is shown to terminate, and the proof-theoretic streng
Autor:
Toshiyasu Arai
Publikováno v:
Archive for Mathematical Logic. 59:257-275
In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions $$\mathsf {g}$$ on ordinals is shown to be equal to the least fixed point of $$\mathsf {g}$$ . Moreover corrections to the previous paper (Arai in Arch M
Autor:
Toshiyasu Arai
Publikováno v:
Annals of Pure and Applied Logic. 169:1246-1269
In this paper we calibrate the strength of the soundness of a set theory KP ω + ( Π 1 -Collection ) with the assumption that ‘there exists an uncountable regular ordinal’ in terms of the existence of ordinals.
Autor:
Toshiyasu Arai
Publikováno v:
Ordinal Analysis with an Introduction to Proof Theory ISBN: 9789811564581
In this chapter we first introduce a standard cut-elimination procedure for the first-order logic and the \(\omega \)-logic, by which we see that the tree-height of the resulting cut-free proofs is bounded by a tower of exponential functions. Such a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9a3a42601e129d54afcb48342f067214
https://doi.org/10.1007/978-981-15-6459-8_3
https://doi.org/10.1007/978-981-15-6459-8_3
Autor:
Toshiyasu Arai
Publikováno v:
The Legacy of Kurt Schütte ISBN: 9783030494230
In this paper we give a terminating cut-elimination procedure for a logic calculus SBL. SBL corresponds to the second order arithmetic Π\( \frac{1}{2} \) Separation and Bar Induction.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6113f68a696abd9aff638a46a98d91ed
https://doi.org/10.1007/978-3-030-49424-7_15
https://doi.org/10.1007/978-3-030-49424-7_15
Autor:
Toshiyasu Arai
Publikováno v:
Ordinal Analysis with an Introduction to Proof Theory ISBN: 9789811564581
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78b087d77d9bc46ea5b86b13d3554590
https://doi.org/10.1007/978-981-15-6459-8_1
https://doi.org/10.1007/978-981-15-6459-8_1
Autor:
Toshiyasu Arai
Publikováno v:
Ordinal Analysis with an Introduction to Proof Theory ISBN: 9789811564581
The sequent calculus \({\textit{\textbf{G}}}_{1}\) for the classical first-order logic in Sect. 1.2 is best seen as a refutation procedure. Inference rules are regarded as searching step of a counter-model of the endsequent when we turn inferences up
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::130b72f036da5d1e4b519a046b928417
https://doi.org/10.1007/978-981-15-6459-8_2
https://doi.org/10.1007/978-981-15-6459-8_2
Autor:
Toshiyasu Arai
Publikováno v:
Logic in Asia: Studia Logica Library ISBN: 9789811564581
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c8bf356bafaa8bf551ffe24058fbfe1b
https://doi.org/10.1007/978-981-15-6459-8
https://doi.org/10.1007/978-981-15-6459-8