Wilkie, A J and Jones, G O (2008) Locally polynomially bounded structures. Bulletin of the London Mathematical Society, 40 (2). pp. 239-248.
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Abstract
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed o-minimal and polynomially bounded reduct. As an application we show that in certain o-minimal structures definable functions are piecewise implicitly defined over the basic functions in the in the language.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | O-minimality |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 26 Real functions |
| Depositing User: | Prof Alex J Wilkie |
| Date Deposited: | 05 Jan 2012 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1744 |
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