Real Algebraic and Analytic Geometry

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343. Krzysztof Jan Nowak:
A counter-example concerning quantifier elimination in quasianalytic structures.


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.

Full text, 17p.: dvi 58k, pdf 287k.

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