Indiscernibles and dimensional compactness

Henson, C. Ward, and Zlatoš, Pavol. "Indiscernibles and dimensional compactness." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 199-203. <http://eudml.org/doc/247915>.

@article{Henson1996,
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 $\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.},
author = {Henson, C. Ward, Zlatoš, Pavol},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {alternative set theory; nonstandard analysis; biequivalence vector space; compact; dimensionally compact; indiscernibles; Ramsey theorem; nonstandard analysis; dimensionally compact; indiscernibles; Ramsey theorem; alternative set theory; biequivalence vector space},
language = {eng},
number = {1},
pages = {199-203},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Indiscernibles and dimensional compactness},
url = {http://eudml.org/doc/247915},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Henson, C. Ward
AU - Zlatoš, Pavol
TI - Indiscernibles and dimensional compactness
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 199
EP - 203
AB - 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.
LA - eng
KW - alternative set theory; nonstandard analysis; biequivalence vector space; compact; dimensionally compact; indiscernibles; Ramsey theorem; nonstandard analysis; dimensionally compact; indiscernibles; Ramsey theorem; alternative set theory; biequivalence vector space
UR - http://eudml.org/doc/247915
ER -