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Preprint Number 1564
1564. Jan Hubička, Matěj Konečný, Jaroslav Nešetřil
All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)
Submission date: 11 February 2019.
In this paper we prove a general theorem showing the extension
partial automorphisms (EPPA, also called the Hrushovski property) for
of structures containing relations and unary functions, optionally equipped
with a permutation group of the language. The proof is elementary,
combinatorial and fully self-contained. Our result is a common
the Herwig-Lascar theorem on EPPA for relational classes with forbidden
homomorphisms, the Hodkinson-Otto theorem on EPPA for relational free
amalgamation classes, its strengthening for unary functions by Evans,
Hubička and Nešetřil and their coherent variants by Siniora and
Solecki. We also prove an EPPA analogue of the main results of J.
and J. Nešetřil: All those Ramsey classes (Ramsey classes with
closures and forbidden homomorphisms), thereby establishing a common
for proving EPPA and the Ramsey property.
Mathematics Subject Classification: 05E18, 20B25, 22F50, 03C52
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