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Locally polynomially bounded structures
Author(s) -
Jones G. O.,
Wilkie A. J.
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn004
Subject(s) - mathematics , kingdom , subject (documents) , library science , computer science , paleontology , biology
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions be definable in a definably complete expansion of a real closed field and be 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 language.