Gianluca Paolini

collaborators

3 papers

math.GR2024

Profinite rigidity of affine Coxeter groups

Gianluca Paolini, Rizos Sklinos

We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this that they are profinitely rigid in the absolute sense. We then show that the first-or…

math.LO2024

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…

math.LO2024

Computable Scott sentences and the weak Whitehead problem for finitely presented groups

Gianluca Paolini

We prove that if $A$ is a computable Hopfian finitely presented structure, then $A$ has a computable $d$ - $Σ_{2}$ Scott sentence if and only if the weak Whitehead problem for $A$ is d…