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Preprint Number 1883

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1883. Gareth Jones and Olivier Le Gal
Powers are easy to avoid

Submission date: 20 November 2020


Suppose that ℝ̃ is an o-minimal expansion of the real field in which restricted power functions are definable. We show that if ℝ̂ is both a reduct (in the sense of definability) of the expansion ℝ̃^ℝ of ℝ̃ by all real power functions and an expansion (again in the sense of definability) of ℝ̃, then, provided that ℝ̃ and ℝ̂ have the same field of exponents, they define the same sets. This can be viewed as a polynomially bounded version of an old conjecture of van den Dries and Miller.

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Full text arXiv 2011.10335: pdf, ps.

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