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Aristotelis Panagiotopoulos

Publications and source records attributed to Aristotelis Panagiotopoulos.

20 records · Page 2Linked to original sources

arXiv2017

Compact spaces as quotients of projective Fraisse limits

We develop a theory of projective Fraisse limits in the spirit of Irwin- Solecki. The structures here will additionally support dual semantics as in [Sl10, Sl12]. Let Y be a compact metrizable space and let G be a closed subgroup of Homeo(Y). We show that there is always a projective Frasse limit K and a closed definable equivalence relation r on K, so that the quotient of K under r is homeomorphic to Y and the projection of K on Y induces a continuous group embedding of Aut(K) into G with dense image.

math.LO↗

arXiv2014

Extentability of Automorphisms of Generic Substructures

We show that if g is a generic (in the sense of Baire category) isometry of a generic subspace of the Urysohn metric space U, then g does not extend to a full isometry of U. The same holds for the Urysohn sphere S. Let M be a Fraisse L-structure, where L is a relational countable language and M has no algebraicity. We provide necessary and sufficient conditions for the following to hold: for a generic substructure A of M, every automorphism f in Aut(A) extends to a full automorphism f in Aut(M). From our analysis, a dichotomy arises and some structural results are derived that, in particular, apply to omega-stable Fraisse structures without algebraicity.

math.LO↗