Generic Expansions of Countable Models

Notre Dame Journal of Formal Logic 53 (4):511-523 (2012)
Abstract
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 $(N,\sigma)$ 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, $(N,\sigma)$ is Truss generic if and only if $(N,\sigma)$ is an e-atomic model. When $T$ is $\omega$ -categorical and $T_{0}$ has a model companion $T_{\mathrm {mc}}$ , the e-atomic models are simply the atomic models of $T_{\mathrm {mc}}$
Keywords generic automorphism   existentially closed structure   comeager conjugacy class
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Adam R. Day (2013). Indifferent Sets for Genericity. Journal of Symbolic Logic 78 (1):113-138.
    Christopher Barney (2003). Ultrafilters on the Natural Numbers. Journal of Symbolic Logic 68 (3):764-784.
    Su Gao (1998). On Automorphism Groups of Countable Structures. Journal of Symbolic Logic 63 (3):891-896.
    Analytics

    Monthly downloads

    Added to index

    2012-11-09

    Total downloads

    2 ( #258,148 of 1,088,400 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,400 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.