Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-11T02:48:39.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Mutually algebraic structures and expansions by predicates

Published online by Cambridge University Press:  12 March 2014

Michael C. Laskowski
Michael C. Laskowski*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA, E-mail: mcl@math.umd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model M of T has an expansion (M, A) by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct. and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 185 - 194
Copyright
Copyright © Association for Symbolic Logic 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baizhanov, B. and Baldwin, J. T., Local homogeneity, this Journal, vol. 69 (2004), pp. 1243–1260.Google Scholar
[2]Baldwin, J. T., Laskowski, M. C., and Shelah, S.. Forcing isomorphism, this Journal, vol. 58 (1993), pp. 1291–1301.Google Scholar
[3]Baldwin, J. T. and Shelah, S., Second-order quantifiers and the complexity of theories, Notre Dame Journal of Formal Logic, vol. 26 (1985), pp. 229–303.CrossRefGoogle Scholar
[4]Dolich, A., Laskowski, M. C., and Raichev, A., Model completeness for trivial, uncountahly categorical theories of Morley rank 1, Archive for Mathematical Logic, vol. 45 (2006), pp. 931–945.CrossRefGoogle Scholar
[5]Laskowski, M. C., The elementary diagram of a trivial, weakly minimal structure is near model complete, Archive for Mathematical Logic, vol. 48 (2009), pp. 15–24.CrossRefGoogle Scholar
[6]Shelah, S., Classification theory, revised ed., North Holland, Amsterdam, 1990.Google Scholar