6 papers
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…
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…
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…
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…