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 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…
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 automor…
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 nat…
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 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…