MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1219

Preprint Number 1219

Previous Next Preprint server


1219. Daoud Siniora, Sławomir Solecki
Coherent extension of partial automorphisms, free amalgamation, and dense locally finite subgroups
E-mail:

Submission date: 4 May 2017

Abstract:

We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite relational structures. Such strengthening yields several combinatorial and group-theoretic consequences. We obtain a “coherent” form of EPPA for free amalgamation classes over a finite relational language. We also get that the isometry group of the rational Urysohn space, the automorphism group of the Fraïssé limit of any Fraïssé class which can be written as the class of all $\mathcal{T}$-free structures (in the Herwig-Lascar sense), and the automorphism group of any free homogeneous structure over a finite relational language, all contain a dense locally finite subgroup. Moreover, using EPPA for free amalgamation classes we show that any free homogeneous structure over a finite relational language admits ample generics.

Mathematics Subject Classification: 03E15, 03C15, 03C13, 05C25, 08A35

Keywords and phrases:

Full text arXiv 1705.01888: pdf, ps.


Last updated: May 15 2017 12:16 Please send your corrections to: