Algebra Seminar talk

2017-10-20 (14:00)
Jan Grebík (Akademie věd České republiky)
Reconstruction of $\omega$-categorical structures from their automorphism groups


By a standard result in model theory a set $A$ is $\emptyset$-definable in an $\omega$-categorical structure $M$ if and only if it is invariant under the action of Aut($M$). That suggests that a lot information about $M$ is coded in Aut($M$). We present two reconstruction theorems that are connected to this philosophy.