Submission date: 30 January 2008.

Abstract:

The paper contains two results. Firstly I prove that every weakly o-minimal expansion of the ordered field of real algebraic numbers is polynomially bounded. The proof uses the strong cell decomposition property, Baizhanov's theorem on expansions of models of weakly o-minimal theories by convex predicates, Miller's dichotomy theorem and Gelfond Schneider theorem. The second result of the paper says that if Schanuel's conjecture is true and K is a real closed subfield of the reals having finite transcendence degree, then every weakly o-minimal expansion of K is polynomially bounded.

Mathematics Subject Classification: 03C64, 11U09

Keywords and phrases: weakly o-minimal structure, polynomially bounded, Gelfond Schneider theorem, Schanuel's conjecture

Full text: pdf, dvi, ps.