Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T19:35:06.104Z Has data issue: false hasContentIssue false
  • English
  • Français

Definable sets in Boolean-ordered o-minimal structures. I

Published online by Cambridge University Press:  12 March 2014

Ludomir Newelski  and
Roman Wencel
Ludomir Newelski
Affiliation:
Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-Mail: newelski@math.uni.wroc.pl
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 prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1821 - 1836
Copyright
Copyright © Association for Symbolic Logic 2001

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]Knight, J., Pillay, A., and Steinhorn, C., Definable sets in ordered structures. II, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 593–605.CrossRefGoogle Scholar
[2]Lascar, D., Stability in model theory, Longman Scientific and Technical, New York, 1986.Google Scholar
[3]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
[4]Pillay, A. and Steinhorn, C., Definable sets in ordered structures. III, Transactions of the American Mathematical Society, vol. 309 (1988), pp. 469–476.CrossRefGoogle Scholar
[5]Toffalori, C., Lattice ordered o-minimal structures, Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 447–463.CrossRefGoogle Scholar