29 citations · 43 across the 29 of their papers we have counts for
44 papers
Kaplansky decompositions of Polish modules
Ivo Herzog, Gianluca Paolini, Saharon Shelah
Let be a countable ring. Given an -module , we call a decomposition a Kaplansky decomposition if each is countable. We characterize th…
Acylindrical Hyperbolicity and Pure Conjugating Automorphisms in Graph Products of Groups
Gianluca Paolini, Jean-Luc Rabideau
We study graph products of groups over defining graphs of arbitrary cardinality from two closely related viewpoints. First, we characterize acylindrical hyperbolicity. If the defin…
The lattice of abstract elementary classes of modules
Tapani Hyttinen, Marcos Mazari-Armida, Gianluca Paolini
Let be a ring. We organize the abstract elementary classes whose underlying class is the class of all -modules and whose strong submodel relation lies between the submodule…
Realizing Non-Archimedean Polish Groups as Outer Automorphism Groups
Gianluca Paolini, Jean-Luc Rabideau
We prove that every non-Archimedean Polish group is topologically isomorphic to the outer automorphism group of a countable discrete group. Furthermore, our construction is Borel.…
On the problem of stability of abstract elementary classes of modules
Gianluca Paolini, Saharon Shelah
It is an open problem of Mazari-Armida whether every abstract elementary class of -modules , with the pure submodule r…
First-order aspects of Artin groups
Alberto Cassella, Gianluca Paolini, Giovanni Paolini
We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if i…
A Galois correspondence for automorphism groups of structures with the Lascar Property
Gianluca Paolini, Federico Pisciotta
Generalizing the -categorical context, we introduce a notion, which we call the Lascar Property, that allows for a fine analysis of the topological isomorphisms between automorp…
A New Construction Principle
Tapani Hyttinen, Gianluca Paolini, Davide Emilio Quadrellaro
We use the framework of Abstract Elementary Classes (s) to introduce a new Construction Principle , which generalises the Construction P…
On the Model Theory of Open Incidence Structures: The Rank 2 Case
Gianluca Paolini, Davide Emilio Quadrellaro
Taking inspiration from [1, 21, 24], we develop a general framework to deal with the model theory of open incidence structures. In this first paper we focus on the study of systems…
-free abelian non-Archimedean Polish groups
Gianluca Paolini, Saharon Shelah
An uncountable -free group cannot admit a Polish group topology but an uncountable -free abelian group can, as witnessed, for example, by the Baer-Specker group…
Oligomorphic groups, their automorphism groups, and the complexity of their isomorphism
Gianluca Paolini, Andre Nies
The paper establishes results following two interconnected directions. 1. Let be a Roelcke precompact closed subgroup of the group of permutations of the natu…
Around first-order rigidity of Coxeter groups
Simon André, Gianluca Paolini
By the work of Sela, for any free group , the Coxeter group is elementarily equivalent to…
Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order
Gianluca Paolini, Saharon Shelah
In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional proper…
The construction principle and non homogeneity of uncountable relatively free groups
Davide Carolillo, Gianluca Paolini
In [11] Sklinos proved that any uncountable free group is not -homogenenous. This was later generalized by Belegradek in [1] to torsion-free residually finite relatively…
Anti-Classification Results for Rigidity Conditions in Abelian and Nilpotent Groups
Gianluca Paolini, Saharon Shelah
Relying on the techniques and ideas from our recent paper [13], we prove several anti-classification results for various rigidity conditions in countable abelian and nilpotent grou…
On the existence of uncountable Hopfian and co-Hopfian abelian groups
Gianluca Paolini, Saharon Shelah
We deal with the problem of existence of uncountable co-Hopfian abelian groups and (absolute) Hopfian abelian groups. Firstly, we prove that there are no co-Hopfian reduced abelian…
Torsion-Free Abelian Groups are Borel Complete
Gianluca Paolini, Saharon Shelah
We prove that the Borel space of torsion-free Abelian groups with domain is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as…
Computable Scott Sentences for Quasi-Hopfian Finitely Presented Structures
Gianluca Paolini
We prove that every quasi-Hopfian finitely presented structure has a - Scott sentence, and that if in addition is computable and satisfies a natural comput…
First-Order Aspects of Coxeter Groups
Bernhard Muhlherr, Gianluca Paolini, Saharon Shelah
We lay the foundations of the first-order model theory of Coxeter groups. Firstly, with the exception of the -spherical non-affine case (which we leave open), we characterize th…
Strongly Minimal Steiner Systems I: Existence
John Baldwin, Gianluca Paolini
A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner -system (for ) is a linear space such that each lin…
First-Order Model Theory of Free Projective Planes
Tapani Hyttinen, Gianluca Paolini
We prove that the theory of open projective planes is complete and strictly stable, and infer from this that Marshall Hall's free projective planes are al…
Some Results on Polish Groups
Gianluca Paolini, Saharon Shelah
We prove that no quantifier-free formula in the language of group theory can define the -half graph in a Polish group, thus generalising some results from [6]. We then po…
On a Cardinal Invariant Related to the Haar Measure Problem
Gianluca Paolini, Saharon Shelah
In [6], given a metrizable profinite group , a cardinal invariant of the continuum was introduced, and a positive solution to the Haar Measure Problem for …
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…