Real Algebraic and Analytic Geometry
Submission: 2013, June 8.
This paper provides an example of a quasianalytic structure which does not admit quantifier elimination in the language of restricted quasianalytic functions augmented by the reciprocal function $1/x$. Our construction applies rectilinearization of terms as well as some theorems on power substitution for Denjoy--Carleman classes and on non-extendability of quasianalytic germs.
Mathematics Subject Classification (2010): 03C10, 26E10, 03C64.
Keywords and Phrases: quasianalytic structures, quantifier elimination, Denjoy--Carleman classes.
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