Application of Quantifier Elimination in Banach Spaces

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.