10 papers · 1 filter
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…
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 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…
-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…
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…