On ω-independence and the Kunen-Shelah property
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2002
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Cambridge Univ Press
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Suátrez Granero, A., Jiménez Sevilla, M. M., Moreno, J. P. «ON $\omega$-INDEPENDENCE AND THE KUNEN–SHELAH PROPERTY». Proceedings of the Edinburgh Mathematical Society, vol. 45, n.o 2, junio de 2002, pp. 391-95. DOI.org (Crossref), https://doi.org/10.1017/S0013091500001061.
Abstract
We prove that spaces with an uncountable omega-independent family fail the Kunen-Shelah property. Actually, if {x(i)}(iis an element ofI) is an uncountable w-independent family, there exists an uncountable subset J.C I such that x(j) is not an element of (conv) over bar({x(i)}(iis an element ofj/{j}) for every j is an element of J. This improves a previous result due to Sersouri, namely that every uncountable omega-independent family contains a convex right-separated subfamily.
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Supported in part by DGICYT grants PB 97-0240 and BMF2000-0609.