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Equimorphy versus Isomorphy

Banff International Research Station for Mathematical Innovation and Discovery

Joint work wih Claude Laflamme, Norbert Sauer and Robert Woodrow. Two structures are said to be $\emph{equimorphic}$ if each embeds into the other. I will report on two conjectures about the number of structures (counted up to isomorphy) which are equimorphic to a given structure; one by Bonato and Tardif asking whether the number of trees equimorphic of a given tree is either $1$ or is infinite, the other by Thomass\'e asking a similar question for relational structures. I will present a positive answer of Thomass'e's conjecture for chains and for countable homogeneous structures (whose automorphism group is oligomorphic). I will conclude by some results about the hypergraph of copies of a countable homogeneous structure.

Mathematics; Combinatorics; Dynamical systems and ergodic theory; Logic and foundations

video/mp4

Author affiliation: University Claude-Bernard, Lyon 1

2016-05-12

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58125

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/