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Application of Quantifier Elimination in Banach Spaces

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Siu-Ah Ng

We consider applications of quantifier elimination ({\em QE}) from our

study of logical properties of Banach spaces. Roughly speaking, a Banach

space satisfies {\em QE} if complicated definitions of sets in such

space can be replaced by simpler ones that do not use existential nor

universal quantifications. Among the applications are reflexivity,

convexity and isometry properties for Banach spaces that satisfy {\em

QE}. Particular attention is given to those spaces constructed by the

nonstandard hull method.