Consequences of neocompact quantifier elimination

Abstract

Key words Banach space structures, quantifier elimination, neocompact, positive bounded formula, nonstandard hull. MSC (2000)03C10, 03H05, 03C65, 46B08, 46B04We provide some consequences of a Quantifier Elimination Property and related properties previously introduced (see [4]) in the setting of Banach space structures. We further consider some applications of quantifierfree definability, such as strict convexity via the definability of certain mapping and the continuity of definable functions.