Zobrazeno 1 - 10
of 158
pro vyhledávání: '"MARCONE, ALBERTO"'
Autor:
Marcone, Alberto, Osso, Gian Marco
This paper classifies different fragments of the Galvin-Prikry theorem, an infinite dimensional generalization of Ramsey's theorem, in terms of their uniform computational content (Weihrauch degree). It can be seen as a continuation of arXiv:2003.042
Externí odkaz:
http://arxiv.org/abs/2410.06928
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
Given a nonempty set $\mathcal{L}$ of linear orders, we say that the linear order $L$ is $\mathcal{L}$-convex embeddable into the linear order $L'$ if it is possible to partition $L$ into convex sets indexed by some element of $\mathcal{L}$ which are
Externí odkaz:
http://arxiv.org/abs/2312.01198
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of circular or
Externí odkaz:
http://arxiv.org/abs/2309.09910
It has recently been shown that fairly strong axiom systems such as $\mathsf{ACA}_0$ cannot prove that the antichain with three elements is a better quasi order ($\mathsf{bqo}$). In the present paper, we give a complete characterization of the finite
Externí odkaz:
http://arxiv.org/abs/2305.01066
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
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:
The Journal of Symbolic Logic 89 (2024), 262-307
We analyze the axiomatic strength of the following theorem due to Rival and Sands in the style of reverse mathematics. "Every infinite partial order $P$ of finite width contains an infinite chain $C$ such that every element of $P$ is either comparabl
Externí odkaz:
http://arxiv.org/abs/2107.02531
Autor:
Fiori-Carones, Marta, Marcone, Alberto
Publikováno v:
Discrete Mathematics 345 (2022), article 112935
Interval graphs and interval orders are deeply linked. In fact, edges of an interval graphs represent the incomparability relation of an interval order, and in general, of different interval orders. The question about the conditions under which a giv
Externí odkaz:
http://arxiv.org/abs/2101.09111
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