Barbina, Silvia and Zambella, Domenico
|DOI (Digital Object Identifier) Link:||http://doi.org/10.1215/00294527-1722728|
|Google Scholar:||Look up in Google Scholar|
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 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.
|Item Type:||Journal Article|
|Copyright Holders:||2012 University of Notre Dame|
|Keywords:||generic automorphism; existentially closed structure; comeagre conjugacy class|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
|Depositing User:||Silvia Barbina|
|Date Deposited:||31 Jan 2012 16:11|
|Last Modified:||18 Jan 2016 11:59|
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