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Combinatorial images of sets of reals and semifilter trichotomy

Published online by Cambridge University Press:  12 March 2014

Boaz Tsaban  and
Lyubomyr Zdomskyy
Boaz Tsaban
Affiliation:
Bar-Ilan University, Department of Mathematics, Ramat-Gan 52900, Israeland, Weizmann Institute of Science, Department of Mathematics, Rehovot 76100, Israel, E-mail: tsaban@math.biu.ac.il, URL: http://www.cs.biu.ac.il/~tsaban
Lyubomyr Zdomskyy*
Affiliation:
Ivan Franko Lviv National University, Department of Mechanics and Mathematics, Universytetska 1, LVIV 79000, Ukraine, and, Weizmann Institute of Science, Department of Mathematics, Rehovot 76100, Israel
*
Kurt Gödel Research Center for Mathematical Logic, Währinger Str. 25, A-1090, Vienna, Austria, E-mail: lzdomsky@gmail.com
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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.

Keywords

scheepers propertysemifilter trichotomy
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1278 - 1288
Copyright
Copyright © Association for Symbolic Logic 2008

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