Order with successors is not interprétable in RCF

S. Świerczkowski

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 3, page 281-285
  • ISSN: 0016-2736

Abstract

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Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.

How to cite

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Świerczkowski, S.. "Order with successors is not interprétable in RCF." Fundamenta Mathematicae 143.3 (1993): 281-285. <http://eudml.org/doc/212009>.

@article{Świerczkowski1993,
abstract = {Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.},
author = {Świerczkowski, S.},
journal = {Fundamenta Mathematicae},
keywords = {interpretation; real closed field; first-order theory of linear order; successor; real number field},
language = {eng},
number = {3},
pages = {281-285},
title = {Order with successors is not interprétable in RCF},
url = {http://eudml.org/doc/212009},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Świerczkowski, S.
TI - Order with successors is not interprétable in RCF
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 3
SP - 281
EP - 285
AB - Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.
LA - eng
KW - interpretation; real closed field; first-order theory of linear order; successor; real number field
UR - http://eudml.org/doc/212009
ER -

References

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  1. [1] L. van den Dries, Algebraic theories with definable Skolem functions, J. Symbolic Logic 49 (1984), 625-629. Zbl0596.03032
  2. [2] L. van den Dries, Definable sets in O-minimal structures, lecture notes at the University of Konstanz, spring 1985. 
  3. [3] L. van den Dries, Tame Topology and O-minimal Structures, book in preparation. 
  4. [4] J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Math. Logik Grundlag. Math. 31 (1985), 449-460. Zbl0559.03034
  5. [5] J. Mycielski, A lattice connected with relative interpretability of theories, J. Symbolic Logic 42 (1977), 297-305. Zbl0371.02026
  6. [6] J. Mycielski, P. Pudlák and A. Stern, A lattice of chapters of mathematics, Mem. Amer. Math. Soc. 426 (1991). Zbl0696.03030
  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. Stern, The lattice of local interpretability of theories, Ph.D. Thesis, University of California, Berkeley, March 1984. 
  9. [9] A. Stern and S. Świerczkowski, A class of connected theories of order, J. Symbolic Logic, to appear. Zbl0805.03048

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