Generic expansions of countable models

TL;DR

This paper compares two notions of generic expansions of countable saturated structures, one based on model theory and amalgamation, and the other on topological Baire category properties, extending Truss's automorphism framework.

Contribution

It introduces a comparison between model-theoretic and topological notions of genericity for expansions, generalizing Truss's automorphism approach to finite tuples.

Findings

Two distinct notions of generic expansion are compared.

The topological notion is extended to finite tuples of predicates and functions.

The relationship between the two notions is clarified.

Abstract

We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to model-companions and to amalgamation constructions \'a la Hrushovski-Fra\"iss\'e. Another notion of generic expansion is defined via topological properties and Baire category theory. The second type of genericity was first formulated by Truss for automorphisms. We work with a later generalization, due to Ivanov, to finite tuples of predicates and functions.