# A note on noninterpretability in o-minimal structures

Fundamenta Mathematicae (1998)

- Volume: 158, Issue: 1, page 19-22
- ISSN: 0016-2736

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topBianconi, Ricardo. "A note on noninterpretability in o-minimal structures." Fundamenta Mathematicae 158.1 (1998): 19-22. <http://eudml.org/doc/212298>.

@article{Bianconi1998,

abstract = {We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.},

author = {Bianconi, Ricardo},

journal = {Fundamenta Mathematicae},

keywords = {-minimal structure; pre-ordered structure with successors; dense order; interpretability},

language = {eng},

number = {1},

pages = {19-22},

title = {A note on noninterpretability in o-minimal structures},

url = {http://eudml.org/doc/212298},

volume = {158},

year = {1998},

}

TY - JOUR

AU - Bianconi, Ricardo

TI - A note on noninterpretability in o-minimal structures

JO - Fundamenta Mathematicae

PY - 1998

VL - 158

IS - 1

SP - 19

EP - 22

AB - We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.

LA - eng

KW - -minimal structure; pre-ordered structure with successors; dense order; interpretability

UR - http://eudml.org/doc/212298

ER -

## References

top- [1] L. van den Dries, Tame Topology and O-minimal Structures, London Math. Soc. Lecture Note Ser. 248, Cambridge Univ. Press, 1998.
- [2] J. Knight, A. Pillay and C. Steinhorn, Definable sets in ordered structures II, Trans. Amer. Math. Soc. 295 (1986), 593-605. Zbl0662.03024
- [3] J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Logik Grundlagen Math. 31 (1985), 449-460. Zbl0559.03034
- [4] J. Mycielski, P. Pudlák and A. Stern, A lattice of chapters of mathematics (interpretations between theorems), Mem. Amer. Math. Soc. 426 (1990). Zbl0696.03030
- [5] A. Pillay, Some remarks on definable equivalence relations in o-minimal structures, J. Symbolic Logic 51 (1986), 709-714. Zbl0632.03028
- [6] A. Pillay and C. Steinhorn, Discrete o-minimal structures, Ann. Pure Appl. Logic 34 (1987), 275-289.
- [7] A. Pillay and C. Steinhorn, Definable sets in ordered structures I, Trans. Amer. Math. Soc. 295 (1986), 565-592. Zbl0662.03023
- [8] A. Pillay and C. Steinhorn, Definable sets in ordered structures III, ibid. 309 (1988), 469-476. Zbl0707.03024
- [9] S. Świerczkowski, Order with successors is not interpretable in RCF, Fund. Math. 143 (1993), 281-285. Zbl0794.03018

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