Geodesic
Indiscernibles and dimensional compactness
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 199-203

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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 $\langle W,M,G\rangle$, 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. Náter, P. Pulmann and the second author.
Classification : 03H05, 46A99, 46S10, 46S20
Keywords: alternative set theory; nonstandard analysis; biequivalence vector space; compact; dimensionally compact; indiscernibles; Ramsey theorem 
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Henson, C. Ward; Zlatoš, Pavol. Indiscernibles and dimensional compactness. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 199-203. http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a13/