Journal of Symbolic Logic

Combinatorial images of sets of reals and semifilter trichotomy

Boaz Tsaban and Lyubomyr Zdomskyy

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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.

Article information

J. Symbolic Logic, Volume 73, Issue 4 (2008), 1278-1288.

First available in Project Euclid: 27 December 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: Primary: 03E17 Secondary: 37F20.

Scheepers property semifilter trichotomy


Tsaban, Boaz; Zdomskyy, Lyubomyr. Combinatorial images of sets of reals and semifilter trichotomy. J. Symbolic Logic 73 (2008), no. 4, 1278--1288. doi:10.2178/jsl/1230396918.

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