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 Publications > Preprint server > Preprint Number 1219 Preprint Number 1219 1219. Daoud Siniora, Sławomir Solecki Coherent extension of partial automorphisms, free amalgamation, and dense locally finite subgroups E-mail: (email address protected by JavaScript. Please enable JavaScript to contact) 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.

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