11 citations · 29 across the 12 of their papers we have counts for
12 papers
Computably discrete represented spaces
Eike Neumann, Arno Pauly, Cécilia Pradic +1
In computable topology, a represented space is called computably discrete if its equality predicate is semidecidable. While any such space is classically isomorphic to an initial s…
Chains and antichains in the Weihrauch lattice
Steffen Lempp, Alberto Marcone, Manlio Valenti
We study the existence and the distribution of "long" chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have…
A jump operator on the Weihrauch degrees
Uri Andrews, Steffen Lempp, Alberto Marcone +2
A partial order admits a jump operator if there is a map that is strictly increasing and weakly monotone. Despite its name, the jump in the Weihrauch la…
The weakness of finding descending sequences in ill-founded linear orders
Jun Le Goh, Arno Pauly, Manlio Valenti
We explore the Weihrauch degree of the problems ``find a bad sequence in a non-well quasi order'' () and ``find a descending sequence in an ill-founded linear order''…
The tree pigeonhole principle in the Weihrauch degrees
Damir Dzhafarov, Reed Solomon, Manlio Valenti
We study versions of the tree pigeonhole principle, , in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensi…
Minimal covers in the Weihrauch degrees
Steffen Lempp, Joseph S. Miller, Arno Pauly +2
In this paper, we study the existence of minimal covers and strong minimal covers in the Weihrauch degrees. We characterize when a problem is a minimal cover or strong minimal…
The Weihrauch lattice at the level of : the Cantor-Bendixson theorem
Vittorio Cipriani, Alberto Marcone, Manlio Valenti
This paper continues the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. In particular, we consider problems related to…
Categorifying computable reducibilities
Davide Trotta, Manlio Valenti, Valeria de Paiva
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notion…
Algebraic properties of the first-order part of a problem
Giovanni Solda, Manlio Valenti
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…
Effective aspects of Hausdorff and Fourier dimension
Alberto Marcone, Manlio Valenti
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 $\mat…
Finding descending sequences through ill-founded linear orders
Jun Le Goh, Arno Pauly, Manlio Valenti
In this work we investigate the Weihrauch degree of the problem of finding an infinite descending sequence through a given ill-founded linear order, which is shared b…
On the descriptive complexity of Salem sets
Alberto Marcone, Manlio Valenti
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 of compact subsets of a…