Neocompact quantifier elimination in structures based on Banach spaces Original Research Article

We study conditions for structures based on Banach spaces having the property that each set definable by neocompact formula (certain infinitary formula) is equivalent to the countable intersection of sets definable by quantifier-free formulas. We show that this property is invariant with respect to different nonstandard hull constructions and it is the same as Hensonʹs Quantifier Elimination in sufficiently saturated nonstandard hulls of internal Banach spaces.