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December 2008 Combinatorial images of sets of reals and semifilter trichotomy
Boaz Tsaban, Lyubomyr Zdomskyy
J. Symbolic Logic 73(4): 1278-1288 (December 2008). DOI: 10.2178/jsl/1230396918

Abstract

Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the Hurewicz 1927 problem is positive, it is shown here that semifilter trichotomy implies a negative answer to a slightly stronger form of this problem.

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Boaz Tsaban. Lyubomyr Zdomskyy. "Combinatorial images of sets of reals and semifilter trichotomy." J. Symbolic Logic 73 (4) 1278 - 1288, December 2008. https://doi.org/10.2178/jsl/1230396918

Information

Published: December 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1158.03033
MathSciNet: MR2467216
Digital Object Identifier: 10.2178/jsl/1230396918

Subjects:
Primary: Primary: 03E17 , Secondary: 37F20.

Keywords: Scheepers property , semifilter trichotomy

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 4 • December 2008
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