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pro vyhledávání: '"Arai, Toshiyasu"'
Autor:
Arai, Toshiyasu
In this paper we give an ordinal analysis of a set theory with $\Pi_{N}$-Collection.
Externí odkaz:
http://arxiv.org/abs/2311.12459
Autor:
Arai, Toshiyasu
In the lecture notes it is shown that an ordinal $\psi_{\Omega}(\varepsilon_{\mathbb{S}^{+}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\omega+(M\prec_{\Sigma_{1}}V)$. In this note we show that ${\sf KP}\omega+(M\p
Externí odkaz:
http://arxiv.org/abs/2304.03851
Autor:
Arai, Toshiyasu
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
Comment: arXiv admin note: substantial text overlap with arXiv:2112.09871
Comment: arXiv admin note: substantial text overlap with arXiv:2112.09871
Externí odkaz:
http://arxiv.org/abs/2304.00246
Autor:
Arai, Toshiyasu
In this note we show through infinitary derivations that each provably well-founded strict partial order in ${\rm ACA}_{0}$ admits an embedding to an ordinal$<\varepsilon_{0}$.
Externí odkaz:
http://arxiv.org/abs/2303.14271
Autor:
Arai, Toshiyasu
In arXiv:2208.12944 it is shown that an ordinal $\sup_{N<\omega}\psi_{\Omega_{1}}(\varepsilon_{\Omega_{\mathbb{S}+N}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\ell^{r}+(M\prec_{\Sigma_{1}}V)$. In this paper we sh
Externí odkaz:
http://arxiv.org/abs/2211.08619
Autor:
Arai, Toshiyasu
In this paper we give an ordinal analysis of a set theory extending ${\sf KP}\ell^{r}$ with an axiom stating that `there exists a transitive set $M$ such that $M\prec_{\Sigma_{1}}V$'.
Comment: arXiv admin note: text overlap with arXiv:2112.09871
Comment: arXiv admin note: text overlap with arXiv:2112.09871
Externí odkaz:
http://arxiv.org/abs/2208.12944
Autor:
Arai, Toshiyasu
In this paper we give an ordinal analysis of a set theory with $\Pi_{1}$-Collection.
Comment: The paper is contained and extended in the next one `An ordinal analysis of $\Pi_{N}$-collection'
Comment: The paper is contained and extended in the next one `An ordinal analysis of $\Pi_{N}$-collection'
Externí odkaz:
http://arxiv.org/abs/2112.09871
Autor:
Arai, Toshiyasu
We give a refinement of proof-theoretic analysis of the lpo (lexicographic path order) due to W. Buchholz. This note was written in Feb. 5, 2015 when G. Moser visited Japan.
Externí odkaz:
http://arxiv.org/abs/2008.07124
Autor:
Arai, Toshiyasu
This note was written in Jan. 23, 2015 to answer a problem raised by G. Moser, who asked a constructive proof of a theorem by Ferreira-Zantema.
Externí odkaz:
http://arxiv.org/abs/2008.07123