Journal of Symbolic Logic

Combinatorial images of sets of reals and semifilter trichotomy

Boaz Tsaban and Lyubomyr Zdomskyy

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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.

Article information

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

Dates
First available in Project Euclid: 27 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1230396918

Digital Object Identifier
doi:10.2178/jsl/1230396918

Mathematical Reviews number (MathSciNet)
MR2467216

Zentralblatt MATH identifier
1158.03033

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

Keywords
Scheepers property semifilter trichotomy

Citation

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. https://projecteuclid.org/euclid.jsl/1230396918


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