Hostname: page-component-7dd5485656-6kn8j Total loading time: 0 Render date: 2025-10-30T15:25:37.232Z Has data issue: false hasContentIssue false
  • English
  • Français

Small theories of Boolean ordered o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Roman Wencel
Roman Wencel*
Affiliation:
Mathematical Institute, University of Wrocław, PL. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: rwenc@math.uni.wroc.pl
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate small theories of Boolean ordered o-minimal structures. We prove that such theories are ℵ0-categorical. We give a complete characterization of their models up to bi-interpretability of the language. We investigate types over finite sets, formulas and the notions of definable and algebraic closure.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1385 - 1390
Copyright
Copyright © Association for Symbolic Logic 2002

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Baisalov, Y., Small o-minimal theories, preprint.Google Scholar
[2]Mayer, L., Vaught's conjecture for o-minimal theories, this Journal, vol. 53 (1988), pp. 146–159.Google Scholar
[3]Newelski, L. and Wencel, R., Definable sets in Boolean ordered o-minimal structures I, this Journal, vol. 66 (2001), pp. 1821–1836.Google Scholar
[4]Pillay, A. and Steinhorn, C., Definable sets in ordered structures I, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 565–592.CrossRefGoogle Scholar
[5]Toffalori, C., Lattice ordered o-minimal structures, Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 447–463.CrossRefGoogle Scholar