[Settfa] A seminar announcement (unusual time and place)

Wieslaw Kubis (CAS) kubis at math.cas.cz
Wed Aug 11 11:53:05 CEST 2021

Dear all,

I would like to announce an spontaneous seminar talk (see below for 
details) this Friday 13.08.2021, 15:00, Blue Lecture Room (rear building 
of the IM CAS, Zitna 25).
Everybody is welcome to attend.

Best wishes,

SPEAKER: Andrés Aranda (Charles University)
TITLE: A uniform approach to Fraïssé theorems for 
homomorphism-homogeneous structures

ABSTRACT:  A relational structure M is ultrahomogeneous if every partial 
isomorphism with finite domain is restriction of an automorphism of M. 
Fraïssé's theorem establishes a correspondence between ultrahomogeneous 
structures and classes of finite structures that satisfy the 
Amalgamation Property (and a few more necessary conditions). In 2002, 
Cameron and Nešetřil introduced the notion of homomorphism-homogeneity, 
where homomorphisms with finite domain are restrictions of endomorphisms 
of M. A few years later, Lockett and Truss introduced distinctions 
depending on the type of finite-domain homomorphism and the type of 
endomorphism extending it, resulting in 18 "classical" classes of 
homomorphism-homogeneous structures.

In 2017, Coleman proved Fraïssé theorems for 12 of the 18 notions of 
homogeneity introduced by Lockett and Truss. The problem of finding 
amalgamation properties and Fraïssé theorems for the remaining six 
classes was left open.

Through the example of IB-homogeneity, I will present a method that is 
general enough to identify the amalgamation properties and uniqueness 
conditions for each of the 18 classical homogeneity notions.

More information about the Settfa mailing list