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On Dedekind complete o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Anand Pillay  and
Charles Steinhorn
Anand Pillay
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Charles Steinhorn
Affiliation:
Department of Mathematics, Vassar College, Poughkeepsie, New York 12601
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Abstract

For a countable complete o-minimal theory T, we introduce the notion of a sequentially complete model of T. We show that a model of T is sequentially complete if and only if ≺ for some Dedekind complete model . We also prove that if T has a Dedekind complete model of power greater than , then T has Dedekind complete models of arbitrarily large powers. Lastly, we show that a dyadic theory—namely, a theory relative to which every formula is equivalent to a Boolean combination of formulas in two variables—that has some Dedekind complete model has Dedekind complete models in arbitrarily large powers.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 1 , March 1987 , pp. 156 - 164
Copyright
Copyright © Association for Symbolic Logic 1987

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Footnotes

1

Research partially supported by N.S.F. grant DMS 8401713.

2

Research partially supported by N.S.F. grant DMS 8403137.

References

REFERENCES

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