8 papers
-abstract elementary classes of modules
Roberto Carnevale, Gianluca Paolini
We prove several new results in the theory of -AECs, focusing mainly on (almost) stability, with the primary objective of undertaking a systematic study of -AECs of -modul…
The Construction Principle and superstability of free objects in varieties of algebras
Tapani Hyttinen, Gianluca Paolini, Davide Emilio Quadrellaro
We investigate the relationship between the Eklof-Mekler-Shelah Construction Principle for a variety of algebras and the question of superstability of the free objects…
Borel completeness of Tits buildings with no rank 3 residues of spherical type
Gianluca Paolini, Davide Emilio Quadrellaro
We prove that, for every Coxeter diagram with no rank residues of spherical type and such that has not only edges labelled by , the space of countable (Tits) buildin…
Elementary properties of free lattices III: Undecidability of the full theory
J. B. Nation, Gianluca Paolini
In [6] we proved that the universal theory of infinite free lattices is (algorithmically) decidable, leaving open the problem of decidability of the full theory of an (infinite) fr…
Elementary properties of free lattices II: Decidability of the universal theory
J. B. Nation, Gianluca Paolini
We continue our work on the model theory of free lattices, solving two of the main open problems from our first paper on the subject. Our main result is that the universal (existen…
The Isomorphism Problem for Oligomorphic Groups with Weak Elimination of Imaginaries
Gianluca Paolini
In [21] it was asked if equality on the reals is sharp as a lower bound for the complexity of topological isomorphism between oligomorphic groups. We prove that under the assumptio…
Computable Scott sentences and the weak Whitehead problem for finitely presented groups
Gianluca Paolini
We prove that if is a computable Hopfian finitely presented structure, then has a computable - Scott sentence if and only if the weak Whitehead problem for is d…
Elementary Properties of Free Lattices
J. B. Nation, Gianluca Paolini
We start a systematic analysis of the first-order model theory of free lattices. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as th…