Barbina, Silvia and Zambella, Domenico
(2012).
URL:  http://projecteuclid.org/euclid.ndjfl/1352383229 

DOI (Digital Object Identifier) Link:  http://doi.org/10.1215/002945271722728 
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Abstract
We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, 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,σ be a countable saturated model of some complete theory T, and let (N,σ) denote an expansion of N to the signature L_{0} which is a model of some universal theory T_{0}. We prove that when all existentially closed models of T_{0} have the same existential theory, (N,σ) is Truss generic if and only if (N,σ) is an eatomic model. When T is ωcategorical and T_{0} has a model companion T_{mc}, the eatomic models are simply the atomic models of T_{mc}.
Item Type:  Journal Article 

Copyright Holders:  2012 University of Notre Dame 
ISSN:  00294527 
Keywords:  generic automorphism; existentially closed structure; comeagre conjugacy class 
Academic Unit/Department:  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) 
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Item ID:  31551 
Depositing User:  Silvia Barbina 
Date Deposited:  31 Jan 2012 16:11 
Last Modified:  04 Oct 2016 11:12 
URI:  http://oro.open.ac.uk/id/eprint/31551 
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