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The Isomorphism Problem for Oligomorphic Groups with Weak Elimination of Imaginaries by Paolini, Gianluca is a scholarly article available to read on EtoBox.

What is The Isomorphism Problem for Oligomorphic Groups with Weak Elimination of Imaginaries about?

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 assumption of weak elimination of imaginaries this is indeed the case. Our methods are model theoretic and they also have applications on the classical problem of reconstruction of isomorphisms of permutation groups from (topological) isomorphisms of automorphisms groups. As a concrete application, we give an explicit description of $\mathrm{Aut}(\mathrm{GL}(V))$ for any vector space $V$ of dimension $\aleph_0$ over a finite field, in affinity with the classical description for finite dimensional spaces due to Schreier and van der Waerden.

Author

Paolini, Gianluca

Published

2024

Language

EN