Homomorphism and embedding universal structures for restricted classes

Details Homomorphism and embedding universal structures for restricted classes Homomorphism and embedding universal structures for restricted classes

2009-09-27

arxiv.org/abs/0909.4939v1

Mathematics

Combinatorics

28 pages, 5 figures

Scientific paper

This paper unifies problems and results related to (embedding) universal and homomorphism universal structures. On the one side we give a new combinatorial proof of the existence of universal objects for homomorphism defined classes of structures (thus reproving a result of Cherlin, Shelah and Shi) and on the other side this leads to the new proof of the existence of dual objects (established by Nesetril and Tardif). Our explicite approach has further applications to special structures such as variants of the rational Urysohn space. We also solve a related extremal problem which shows the optimality (of the used lifted arities) of our construction. Our method also relates to weakly indivisible homomorphism defined classes of structures.

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