5 papers · 1 filter
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…
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…
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…