A Fraisse theorem for IB-homogeneous relational structures

Teoria modeli
Osoba referująca: 
Andrés Aranda (TU Dresden)
Data spotkania seminaryjnego: 
środa, 4. Grudzień 2019 - 16:15
Fix a finite relational language $L$. An $L$-structure $M$ is called ultrahomogeneous if every isomorphism between finite induced substructures is restriction of an automorphism of $M$. Ultrahomogeneous $L$-structures have $\omega$-categorical theories with elimination of quantifiers and large automorphism groups with a finite number of orbits on tuples of any finite length $n$, so they are of interest in group theory and model theory.

The classical Fraisse theorem establishes a correspondence between ultrahomogeneous structures and classes of finite structures satisfying, in addition to the obvious restrictions, the joint embedding property and the amalgamation property.

In the early 2000s, the notion of homomorphism-homogeneity was introduced by Cameron and Nesetril, with further refinements by Lockett and Truss. In total, there are $18$ natural classes of homomorphism-homogeneous structures, but Fraisse theorems were not known for most of them until Coleman's work from last year, in which Fraisse theorems were identified and proved for $12$ of the $18$ classes. In this talk, I will present a Fraisse theorem for structures in which any isomorphism between finite substructures is restriction of a global bijective monomorphism.