ArticleOriginal scientific text
Title
Order with successors is not interprétable in RCF
Authors 1
Affiliations
- Department of Mathematics and Computing, P.O. Box 36 - Al Khod - Pc123, Sultan Qaboos University, Muscat, Sultanate of Oman
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.
Bibliography
- L. van den Dries, Algebraic theories with definable Skolem functions, J. Symbolic Logic 49 (1984), 625-629.
- L. van den Dries, Definable sets in O-minimal structures, lecture notes at the University of Konstanz, spring 1985.
- L. van den Dries, Tame Topology and O-minimal Structures, book in preparation.
- J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Math. Logik Grundlag. Math. 31 (1985), 449-460.
- J. Mycielski, A lattice connected with relative interpretability of theories, J. Symbolic Logic 42 (1977), 297-305.
- J. Mycielski, P. Pudlák and A. Stern, A lattice of chapters of mathematics, Mem. Amer. Math. Soc. 426 (1991).
- A. Pillay and C. Steinhorn, Definable sets in ordered structures I, Trans. Amer. Math. Soc. 295 (1986), 565-592.
- A. Stern, The lattice of local interpretability of theories, Ph.D. Thesis, University of California, Berkeley, March 1984.
- A. Stern and S. Świerczkowski, A class of connected theories of order, J. Symbolic Logic, to appear.
Additional information
http://matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14337.pdf
Pages:
281-285
Main language of publication
English
Received
1993-03-05
Published
1993
Exact and natural sciences