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A model-theoretic version of the complement theorem

Nowak K.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

345-353

This paper deals with an axiomatic theory T[sub an] and the expansion R[sub an] of the ordered field of reals, formed by attaching the restricted analytic functions. We show that the theory T[sub an] is model-complete, which may be regarded as a version of Gabrielov's complement theorem. Our proof is based on Robinson's test and it does not involve a partition technique. An immediate corollary is that T[sub an] coincides with the semantic theory Th(R[sub an]) of all sentences true in the structure R[sub an].