2012.4: Locally polynomially bounded structures
2012.4: A J Wilkie and G O Jones (2008) Locally polynomially bounded structures. Bulletin of the London Mathematical Society, 40 (2). pp. 239-248.
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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.
|Subjects:||MSC 2000 > 03 Mathematical logic and foundations|
MSC 2000 > 26 Real functions
|Deposited By:||Prof Alex J Wilkie|
|Deposited On:||05 January 2012|