100 citations · 264 across the 34 of their papers we have counts for
34 papers
Isometry groups of Polish ultrametric spaces
Riccardo Camerlo, Alberto Marcone, Luca Motto Ros
We solve a long-standing open problem, formulated by Krasner in the 1950's, in the context of Polish (i.e. separable complete) ultrametric spaces by providing a characterization of…
Computability of a Whitney Extension
Andrea Brun, Guido Gherardi, Alberto Marcone
We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if is a closed set represented s…
Piecewise convex embeddability on linear orders
Martina Iannella, Alberto Marcone, Luca Motto Ros +1
Given a nonempty set of linear orders, we say that the linear order is -convex embeddable into the linear order if it is possible to partition $…
Convex Embeddability and Knot Theory
Martina Iannella, Alberto Marcone, Luca Motto Ros +1
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-theoret…
Provable better quasi orders
Anton Freund, Alberto Marcone, Fedor Pakhomov +1
It has recently been shown that fairly strong axiom systems such as cannot prove that the antichain with three elements is a better quasi order (). I…
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…
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…
(Extra)ordinary equivalences with the ascending/descending sequence principle
Marta Fiori-Carones, Alberto Marcone, Paul Shafer +1
We analyze the axiomatic strength of the following theorem due to Rival and Sands in the style of reverse mathematics. "Every infinite partial order of finite width contains an…
Uniquely orderable interval graphs
Marta Fiori-Carones, Alberto Marcone
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 differen…
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…
The open and clopen Ramsey theorems in the Weihrauch lattice
Alberto Marcone, Manlio Valenti
We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to from the…
To reorient is easier than to orient: an on-line algorithm for reorientation of graphs
Marta Fiori-Carones, Alberto Marcone
We define an on-line (incremental) algorithm that, given a (possibly infinite) pseudo-transitive oriented graph, produces a transitive reorientation. This implies that a theorem of…
Searching for an analogue of ATR in the Weihrauch lattice
Takayuki Kihara, Alberto Marcone, Arno Pauly
There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to transl…
Polish metric spaces with fixed distance set
Riccardo Camerlo, Alberto Marcone, Luca Motto Ros
We study Polish spaces for which a set of possible distances is fixed in advance. We determine, depending on the properties of , the complexity of the…
Projection operators in the Weihrauch lattice
Guido Gherardi, Alberto Marcone, Arno Pauly
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice c…
The reverse mathematics of wqos and bqos
Alberto Marcone
In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the co…
Linear orders: when embeddability and epimorphism agree
Riccardo Camerlo, Raphaël Carroy, Alberto Marcone
When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective line…
The logic of the reverse mathematics zoo
Giovanna D'Agostino, Alberto Marcone
Building on previous work by Mummert, Saadaoui and Sovine, we study the logic underlying the web of implications and nonimplications which constitute the so called reverse mathemat…
Reverse mathematics, well-quasi-orders, and Noetherian spaces
Emanuele Frittaion, Matt Hendtlass, Alberto Marcone +2
A quasi-order induces two natural quasi-orders on , but if is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Gou…
On isometry and isometric embeddability between ultrametric Polish spaces
Riccardo Camerlo, Alberto Marcone, Luca Motto Ros
We study the complexity with respect to Borel reducibility of the relations of isometry and isometric embeddability between ultrametric Polish spaces for which a set of possibl…
Epimorphisms between linear orders
Riccardo Camerlo, Raphaël Carroy, Alberto Marcone
We study the relation on linear orders induced by order preserving surjections. In particular we show that its restriction to countable orders is a bqo.
Reverse Mathematics and initial intervals
Emanuele Frittaion, Alberto Marcone
In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of the initial…
Linear extensions of partial orders and Reverse Mathematics
Emanuele Frittaion, Alberto Marcone
We introduce the notion of τ-like partial order, where τis one of the linear order types ω, ω*, ω+ω*, and ζ. For example, being ω-like means that every element has finitely many pr…
Computing Maximal Chains
Alberto Marcone, Antonio Montalbán, Richard A. Shore
In 1967 Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note that all chains in a wpo are well-ordered.) We prove that…