Zobrazeno 1 - 10
of 30
pro vyhledávání: '"VALENTI, MANLIO"'
A partial order $(P,\le)$ admits a jump operator if there is a map $j\colon P \to P$ that is strictly increasing and weakly monotone. Despite its name, the jump in the Weihrauch lattice fails to satisfy both of these properties: it is not degree-theo
Externí odkaz:
http://arxiv.org/abs/2402.13163
We explore the Weihrauch degree of the problems ``find a bad sequence in a non-well quasi order'' ($\mathsf{BS}$) and ``find a descending sequence in an ill-founded linear order'' ($\mathsf{DS}$). We prove that $\mathsf{DS}$ is strictly Weihrauch red
Externí odkaz:
http://arxiv.org/abs/2401.11807
We study versions of the tree pigeonhole principle, $\mathsf{TT}^1$, in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics. Two outstanding questions from the
Externí odkaz:
http://arxiv.org/abs/2312.10535
In this paper, we study the existence of minimal covers and strong minimal covers in the Weihrauch degrees. We characterize when a problem $f$ is a minimal cover or strong minimal cover of a problem $h$. We show that strong minimal covers only exist
Externí odkaz:
http://arxiv.org/abs/2311.12676
This paper continues the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. In particular, we consider problems related to perfect subsets of Polish spaces, studying the perfect set theorem, th
Externí odkaz:
http://arxiv.org/abs/2210.15556
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notions lend themselves to a smooth categorical presentation, essentially du
Externí odkaz:
http://arxiv.org/abs/2208.08656
Autor:
Solda, Giovanni, Valenti, Manlio
Publikováno v:
Annals of Pure and Applied Logic Volume 174, Issue 7, July 2023, 103270
In this paper we study the notion of first-order part of a computational problem, first introduced by Dzhafarov, Solomon, and Yokoyama, which captures the "strongest computational problem with codomain $\mathbb{N}$ that is Weihrauch reducible to $f$"
Externí odkaz:
http://arxiv.org/abs/2203.16298
Autor:
Marcone, Alberto, Valenti, Manlio
Publikováno v:
Computability 11 (2022), 299-333
In this paper, we study Hausdorff and Fourier dimension from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity. Working in the hyperspace $\mathbf{K}(X)$ of compact subsets of $X$, with $X=[0,1]^d$ or $X=\mathbb{R
Externí odkaz:
http://arxiv.org/abs/2108.06941
Publikováno v:
J. symb. log. 86 (2021) 817-854
In this work we investigate the Weihrauch degree of the problem $\mathsf{DS}$ of finding an infinite descending sequence through a given ill-founded linear order, which is shared by the problem $\mathsf{BS}$ of finding a bad sequence through a given
Externí odkaz:
http://arxiv.org/abs/2010.03840
Autor:
Marcone, Alberto, Valenti, Manlio
Publikováno v:
Fundamenta Mathematicae 257 (2022), no. 1, 69-94
In this paper we study the notion of Salem set from the point of view of descriptive set theory. We first work in the hyperspace $\mathbf{K}([0,1])$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol{\Pi}^0_3$-compl
Externí odkaz:
http://arxiv.org/abs/2009.09888