Aleksander Ivanov

A countably categorical theory which is not G-compact

We give an example of a countably categorical theory which is not G-compact. The countable model of this theory does not have AZ-enumerations.

An ω-categorical structure with amenable automorphism group

We analyse ω-categorical precompact expansions of particular ω-categorical structures from the viewpoint of amenability of their automorphism groups.We analyse ω-categorical precompact expansions of particular ω-categorical structures from the viewpoint of amenability of their automorphism groups. 2010 Mathematics Subject Classification: 03C15, 03E15

Polish G-spaces and continuous logic

We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker to the case of Polish G-spaces when G is an arbitrary Polish group.

Generating Sym(ω) by Permutations Preserving Dense Orders

We show how generic permutations of ω can be presented by products of permutations preserving dense orders.

The complexity of countable categoricity in finite languages

We study complexity of the index set of countably categorical theories and Ehrenfeucht theories in finite languages.

Degrees of isomorphism types and countably categorical groups

It is shown that for every Turing degree d there is an ω-categorical group G such that the isomorphism type of G is of degree d. We also find an ω-categorical group G such that the isomorphism type of G has no degree.