Order with successors is not interprétable in RCF

• Autorzy: S. Świerczkowski
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 143
• Numer: 3
• Strony: 281-285

Daty

wydano

1993

otrzymano

1993-03-05

Twórcy

autor

S. Świerczkowski

• Department of Mathematics and Computing, P.O. Box 36 - Al Khod - Pc123, Sultan Qaboos University, Muscat, Sultanate of Oman

Bibliografia

• [1] L. van den Dries, Algebraic theories with definable Skolem functions, J. Symbolic Logic 49 (1984), 625-629.
• [2] L. van den Dries, Definable sets in O-minimal structures, lecture notes at the University of Konstanz, spring 1985.
• [3] L. van den Dries, Tame Topology and O-minimal Structures, book in preparation.
• [4] J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Math. Logik Grundlag. Math. 31 (1985), 449-460.
• [5] J. Mycielski, A lattice connected with relative interpretability of theories, J. Symbolic Logic 42 (1977), 297-305.
• [6] J. Mycielski, P. Pudlák and A. Stern, A lattice of chapters of mathematics, Mem. Amer. Math. Soc. 426 (1991).
• [7] A. Pillay and C. Steinhorn, Definable sets in ordered structures I, Trans. Amer. Math. Soc. 295 (1986), 565-592.
• [8] A. Stern, The lattice of local interpretability of theories, Ph.D. Thesis, University of California, Berkeley, March 1984.
• [9] A. Stern and S. Świerczkowski, A class of connected theories of order, J. Symbolic Logic, to appear.