A note on noninterpretability in o-minimal structures

Ricardo Bianconi

Fundamenta Mathematicae (1998)

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

Abstract

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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.

How to cite

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Bianconi, 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

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  1. [1] L. van den Dries, Tame Topology and O-minimal Structures, London Math. Soc. Lecture Note Ser. 248, Cambridge Univ. Press, 1998. 
  2. [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. [3] J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Logik Grundlagen Math. 31 (1985), 449-460. Zbl0559.03034
  4. [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. [5] A. Pillay, Some remarks on definable equivalence relations in o-minimal structures, J. Symbolic Logic 51 (1986), 709-714. Zbl0632.03028
  6. [6] A. Pillay and C. Steinhorn, Discrete o-minimal structures, Ann. Pure Appl. Logic 34 (1987), 275-289. 
  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. Pillay and C. Steinhorn, Definable sets in ordered structures III, ibid. 309 (1988), 469-476. Zbl0707.03024
  9. [9] S. Świerczkowski, Order with successors is not interpretable in RCF, Fund. Math. 143 (1993), 281-285. Zbl0794.03018

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