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ArticleOriginal scientific text

Title

Dense pairs of o-minimal structures

Authors 1

Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A.

Abstract

The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.

Bibliography

  1. L. van den Dries and A. Lewenberg, T-convexity and tame extensions, J. Symbolic Logic 60 (1995), 74-102.
  2. E. Hrushovski, Strongly minimal expansions of algebraically closed fields, Israel J. Math. 79 (1992), 129-151.
  3. A. Macintyre, Dense embeddings I: a theorem of Robinson in a general setting, in: Model Theory and Algebra. A Memorial Tribute to Abraham Robinson; D. H. Saracino and V. B. Weispfenning (eds.), Lecture Notes in Math. 498, Springer, Berlin, 1975, 200-219.
  4. H. D. MacPherson, D. Marker and C. Steinhorn, Weakly o-minimal theories and real closed fields, preprint.
  5. C. Miller and P. Speissegger, Expansions of the real line by open sets: o-minimality and open cores, preprint.
  6. Y. Peterzil and S. Starchenko, A trichotomy theorem for o-minimal structures, Proc. London Math. Soc., to appear.
  7. A. Pillay and C. Steinhorn, Definable sets in ordered structures. I, Trans. Amer. Math. Soc. 295 (1986), 565-592.
  8. A. Robinson, Solution of a problem of Tarski, Fund. Math. 47 (1959), 79-204.
Fundamenta Mathematicae
1998/157/1
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Pages:
61-78
Main language of publication
English
Received
1997-07-24
Accepted
1997-12-30
Published
1998
Exact and natural sciences