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Weakly o-minimal structures and real closed fields
Author(s):
Dugald
Macpherson;
David
Marker;
Charles
Steinhorn
Journal:
Trans. Amer. Math. Soc.
352
(2000),
5435-5483.
MSC (2000):
Primary 03C60, 03C64
Posted:
April 13, 2000
MathSciNet review:
1781273
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Abstract:
A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field is real closed. We also develop a substantial theory of definable sets in weakly o-minimal structures, patterned, as much as possible, after that for o-minimal structures.
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Additional Information:
Dugald
Macpherson
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, U.K.
Email:
pmthdm@amsta.leeds.ac.uk
David
Marker
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
Email:
marker@math.uic.edu
Charles
Steinhorn
Affiliation:
Department of Mathematics, Vassar College, Poughkeepsie, New York 12604
Email:
steinhorn@vassar.edu
DOI:
10.1090/S0002-9947-00-02633-7
PII:
S 0002-9947(00)02633-7
Received by editor(s):
April 24, 1998
Posted:
April 13, 2000
Additional Notes:
The second author's research was partially supported by NSF grant DMS-9626856, and the third author's was partially supported by NSF grants DMS-9401723 and DMS-9704869, and SERC grant GR/H57097
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Copyright
2000,
American Mathematical Society
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