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pro vyhledávání: '"Yokoyama, Keita"'
In this article, we prove that Ramsey's theorem for pairs and two colors is a $\forall \Pi^0_4$ conservative extension of $\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2$, where a $\forall \Pi^0_4$ formula consists of a universal quantifier over sets followed
Externí odkaz:
http://arxiv.org/abs/2404.18974
In this article, we prove that Ramsey's theorem for pairs and two colors is $\Pi^1_1$-conservative over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2 + \mathsf{WF}(\epsilon_0)$ and over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2 + \bigcup_n \mathsf{WF}(\omega^\
Externí odkaz:
http://arxiv.org/abs/2402.11616
Autor:
Suzuki, Yudai, Yokoyama, Keita
The system $\Pi^1_1$-$\mathsf{CA}_0$ is known as the strongest system of the \textit{big five} in reverse mathematics. It is known that some theorems represented by a $\Pi^1_2$ sentence, for example Kruskal's theorem, are provable from $\Pi^1_1$-$\ma
Externí odkaz:
http://arxiv.org/abs/2402.07136
Autor:
Suzuki, Yudai, Yokoyama, Keita
We investigate some Weihrauch problems between $\mathsf{ATR}_2$ and $\mathsf{C}_{\omega^\omega}$ . We show that the fixed point theorem for monotone operators on the Cantor space (a weaker version of the Knaster-Tarski theorem) is not Weihrauch reduc
Externí odkaz:
http://arxiv.org/abs/2305.07321
We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in $\mathsf{RCA}_0$. Furthermore, we show that Caristi's fixed point theorem for both Baire and Borel functions is equivalent to the transfinite leftmost path principle, which
Externí odkaz:
http://arxiv.org/abs/2302.08874
We introduce the notion of the \emph{first-order part} of a problem in the Weihrauch degrees. Informally, the first-order part of a problem $\mathsf{P}$ is the strongest problem with codomaixn $\omega$ that is Weihrauch reducible to $\mathsf{P}$. We
Externí odkaz:
http://arxiv.org/abs/2301.12733
Publikováno v:
The Bulletin of Symbolic Logic, 2023 Sep 01. 29(3), 311-353.
Externí odkaz:
https://www.jstor.org/stable/27253532
We study the parameterized complexity of the problem to decide whether a given natural number $n$ satisfies a given $\Delta_0$-formula $\varphi(x)$; the parameter is the size of $\varphi$. This parameterization focusses attention on instances where $
Externí odkaz:
http://arxiv.org/abs/2211.06121
Autor:
Pacheco, Leonardo, Yokoyama, Keita
It is known that several variations of the axiom of determinacy play important roles in the study of reverse mathematics, and the relation between the hierarchy of determinacy and comprehension are revealed by Tanaka, Nemoto, Montalb\'an, Shore, and
Externí odkaz:
http://arxiv.org/abs/2209.04082
We prove that if $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are countable models of the theory $\mathrm{WKL}^*_0$ such that $\mathrm{I}\Sigma_1(A)$ fails for some $A \in \mathcal{X} \cap \mathcal{Y}$, then $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are iso
Externí odkaz:
http://arxiv.org/abs/2112.10876