Order with successors is not interprétable in RCF
Tom 143 / 1993
Fundamenta Mathematicae 143 (1993), 281-285 DOI: 10.4064/fm-143-3-281-285
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.