# Dense pairs of o-minimal structures

Fundamenta Mathematicae (1998)

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

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topvan 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

top- [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. Zbl0773.12005
- [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. Zbl0946.03045
- [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. Zbl0662.03023
- [8] A. Robinson, Solution of a problem of Tarski, Fund. Math. 47 (1959), 79-204. Zbl0093.01305

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