9 citations · 26 across the 15 of their papers we have counts for
16 papers
Compactness for almost projective modules
Filippo Calderoni, Esmé Yanowitz
In this paper we contribute to the study of compactness properties for algebraic structures. We prove two compactness theorems in the context of almost projective modules from -…
The isomorphism problem for finitely generated bi-orderable groups
Filippo Calderoni, Adam Clay
We analyze the classification problem for finitely generated orderable groups from the viewpoint of descriptive set theory. We analyze the standard Borel space of finitely generate…
Compactness in abelian group theory
Filippo Calderoni, Ava Ostrem
In this paper we discuss large cardinals and compactness theorems in abelian group theory. More specifically, we generalize two classical compactness results for free abelian group…
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…
Forcing, genericity and CBERS
Filippo Calderoni, Dima Sinapova
In this paper we continue the study of equivalence of generics filters started by Smythe in [Smy22]. We fully characterize those forcing posets for which the corresponding equivale…
Condensation and left-orderable groups
Filippo Calderoni, Adam Clay
We discuss condensed left-orderings and develop new techniques to show that the conjugacy relation on the space of left-orderings is not smooth. These techniques apply to the solva…
The Borel complexity of the space of left-orderings, low-dimensional topology, and dynamics
Filippo Calderoni, Adam Clay
We develop new tools to analyze the complexity of the conjugacy equivalence relation , whenever is a left-orderable group. Our methods are used to demonstrate…
Rotation equivalence and cocycle superrigidity
Filippo Calderoni
We analyze Euclidean spheres in higher dimensions and the corresponding orbit equivalence relations induced by the group of rational rotations from the viewpoint of descriptive set…
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…
Borel structures on the space of left-orderings
Filippo Calderoni, Adam Clay
In this paper we study the Borel structure of the space of left-orderings of a group modulo the natural conjugacy action, and by using tools from descriptive s…
Simplicity of the automorphism groups of order and tournament expansions of homogeneous structures
Filippo Calderoni, Aleksandra Kwiatkowska, Katrin Tent
We define the notions of a free fusion of structures and a weakly stationary independence relation. We apply these notions to prove simplicity for the automorphism groups of order…
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…
Invariant universality for projective planes
Filippo Calderoni, Gianluca Paolini
We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desargue…
Invariant universality for quandles and fields
Andrew D. Brooke-Taylor, Filippo Calderoni, Sheila K. Miller
We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are…
The complexity of the embeddability relation between torsion-free abelian groups of uncountable size
Filippo Calderoni
We prove that for every uncountable cardinal such that , the quasi-order of embeddability on the -space of -sized graphs Borel reduces to the embeddability on t…
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…