C. Ward Henson and Pavol Zlato\v{s}
Indiscernibles and dimensional compactness

Abstract:This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set $u S\subseteq G$ in a biequivalence vector space $$, such that $x - y \notin M$ for distinct $x,y \in u$, contains an infinite independent subset. Consequently, a class $X \subseteq G$ is dimensionally compact iff the $\pi $-equivalence $\doteq _M$ is compact on $X$. This solves a problem from the paper [NPZ 1992] by J. N\'ater, P. Pulmann and the second author.

Keywords: alternative set theory, nonstandard analysis, biequivalence vector space, compact, dimensionally compact, indiscernibles, Ramsey theorem
AMS Subject Classification: 46S20, 46S10, 03H05

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