Dense pairs of o-minimal structures

Lou van den Dries

Fundamenta Mathematicae (1998)

  • Volume: 157, Issue: 1, page 61-78
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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van den Dries, Lou. "Dense pairs of o-minimal structures." Fundamenta Mathematicae 157.1 (1998): 61-78. <http://eudml.org/doc/212278>.

@article{vandenDries1998,
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.},
author = {van den Dries, Lou},
journal = {Fundamenta Mathematicae},
keywords = {o-minimal structure; elementary pair; dense pair; small definable set},
language = {eng},
number = {1},
pages = {61-78},
title = {Dense pairs of o-minimal structures},
url = {http://eudml.org/doc/212278},
volume = {157},
year = {1998},
}

TY - JOUR
AU - van den Dries, Lou
TI - Dense pairs of o-minimal structures
JO - Fundamenta Mathematicae
PY - 1998
VL - 157
IS - 1
SP - 61
EP - 78
AB - 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.
LA - eng
KW - o-minimal structure; elementary pair; dense pair; small definable set
UR - http://eudml.org/doc/212278
ER -

References

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  1. [1] L. van den Dries and A. Lewenberg, T-convexity and tame extensions, J. Symbolic Logic 60 (1995), 74-102. 
  2. [2] E. Hrushovski, Strongly minimal expansions of algebraically closed fields, Israel J. Math. 79 (1992), 129-151. Zbl0773.12005
  3. [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. [4] H. D. MacPherson, D. Marker and C. Steinhorn, Weakly o-minimal theories and real closed fields, preprint. 
  5. [5] C. Miller and P. Speissegger, Expansions of the real line by open sets: o-minimality and open cores, preprint. Zbl0946.03045
  6. [6] Y. Peterzil and S. Starchenko, A trichotomy theorem for o-minimal structures, Proc. London Math. Soc., to appear. 
  7. [7] A. Pillay and C. Steinhorn, Definable sets in ordered structures. I, Trans. Amer. Math. Soc. 295 (1986), 565-592. Zbl0662.03023
  8. [8] A. Robinson, Solution of a problem of Tarski, Fund. Math. 47 (1959), 79-204. Zbl0093.01305

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