Notre Dame Journal of Formal Logic

Generic Expansions of Countable Models

Silvia Barbina and Domenico Zambella


We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, and another 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.

Let N be a countable saturated model of some complete theory T, and let (N,σ) denote an expansion of N to the signature L0 which is a model of some universal theory T0. We prove that when all existentially closed models of T0 have the same existential theory, (N,σ) is Truss generic if and only if (N,σ) is an e-atomic model. When T is ω-categorical and T0 has a model companion Tmc, the e-atomic models are simply the atomic models of Tmc.

Article information

Notre Dame J. Formal Logic, Volume 53, Number 4 (2012), 511-523.

First available in Project Euclid: 8 November 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C10: Quantifier elimination, model completeness and related topics
Secondary: 20B27: Infinite automorphism groups [See also 12F10] 03C50: Models with special properties (saturated, rigid, etc.)

generic automorphism existentially closed structure comeager conjugacy class


Barbina, Silvia; Zambella, Domenico. Generic Expansions of Countable Models. Notre Dame J. Formal Logic 53 (2012), no. 4, 511--523. doi:10.1215/00294527-1722728.

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