[Settfa] A seminar announcement (unusual time and place)
Wieslaw Kubis (CAS)
kubis at math.cas.cz
Wed Aug 11 11:53:05 CEST 2021
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.
SPEAKER: Andrés Aranda (Charles University)
TITLE: A uniform approach to Fraïssé theorems for
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
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