17 citations · 51 across the 25 of their papers we have counts for
29 papers
Generalized Descriptive Set Theory at Singular Cardinals of Countable Cofinality
Vincenzo Dimonte, Luca Motto Ros
We provide a comprehensive development of the basics of descriptive set theory for non-separable complete metric spaces whose weight is a singular cardinal of countable confina…
Generalized Borel Sets
Claudio Agostini, Nick Chapman, Luca Motto Ros +1
Generalizing classical descriptive set theory opens foundational questions about the Borel hierarchy. In this paper we systematically study those questions, working in the general…
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…
Structural results on idealistic equivalence relations
Filippo Calderoni, Luca Motto Ros
We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many…
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…
Classification problems from the descriptive set theoretical perspective
Luca Motto Ros
Twenty years have passed since Kechris' seminal survey paper [A. S. Kechris, New directions in descriptive set theory. Bull. Symbolic Logic, 5(2):161-174, 1999]. As a follow-up of…
Anti-classification results for groups acting freely on the line
Filippo Calderoni, David Marker, Luca Motto Ros +1
We explore countable ordered Archimedean groups from the point of view of descriptive set theory. We introduce the space of Archimedean left-orderings for a given…
A descriptive Main Gap Theorem
Francesco Mangraviti, Luca Motto Ros
Answering one of the main questions of [FHK14, Chapter 7], we show that there is a tight connection between the depth of a classifiable shallow theory and the Borel rank of the…
Uncountable structures are not classifiable up to bi-embeddability
Filippo Calderoni, Heike Mildenberger, Luca Motto Ros
Answering some of the main questions from [MR13], we show that whenever is a cardinal satisfying , then the embeddability relation between -sized structures…
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…
Universality of group embeddability
Filippo Calderoni, Luca Motto Ros
Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological…
Can we classify complete metric spaces up to isometry?
Luca Motto Ros
We survey some old and new results concerning the classification of complete metric spaces up to isometry, a theme initiated by Gromov, Vershik and others. All theorems concerning…
Souslin quasi-orders and bi-embeddability of uncountable structures
Alessandro Andretta, Luca Motto Ros
We provide analogues of the results from [FMR11, CMMR13] in the reference list (which correspond to the case ) for arbitrary -Souslin quasi-orders on any Polish space, for…
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…
Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces
Luca Motto Ros, Philipp Schlicht
We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether un…
Bad Wadge-like reducibilities on the Baire space
Luca Motto Ros
We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (…
On the structure of finite level and ω-decomposable Borel functions
Luca Motto Ros
We give a full description of the structure under inclusion of all finite level Borel classes of functions, and provide an elementary proof of the well-known fact that not every Bo…
A new proof of a theorem of Jayne and Rogers
Luca Motto Ros, Brian Semmes
We give a new simpler proof of a theorem of Jayne and Rogers.
The descriptive set-theoretical complexity of the embeddability relation on models of large size
Luca Motto Ros
We show that if κ is a weakly compact cardinal then the embeddability relation on (generalized) trees of size κ is invariantly universal. This means that for every analytic quasi-o…
Some observations on "A new proof of a theorem of Jayne and Rogers"
Miroslav Kačena, Luca Motto Ros, Brian Semmes
We adapt a construction taken from `L. Motto Ros and B. Semmes, A new proof of a theorem of Jayne and Rogers, Real Anal. Exchange 35(1) (2009/2010), 195-204' in order to correct a…
On the complexity of the relations of isomorphism and bi-embeddability
Luca Motto Ros
Given an L_{ω_1 ω}-elementary class C, that is the collection of the countable models of some L_{ω_1 ω}-sentence, denote by \cong_C and \equiv_C the analytic equivalence relations…
Analytic equivalence relations and bi-embedability
Sy-David Friedman, Luca Motto Ros
Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under B…
Game representations of classes of piecewise definable functions
Luca Motto Ros
We present a general way of defining various reduction games on ω which "represent" corresponding topologically defined classes of functions. In particular, we will show how to con…