Journal of Symbolic Logic 73 (4):1278-1288 (2008)

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 property   semifilter trichotomy
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DOI 10.2178/jsl/1230396918
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References found in this work BETA

Groupwise Density and Related Cardinals.Andreas Blass - 1990 - Archive for Mathematical Logic 30 (1):1-11.
Menger's Covering Property and Groupwise Density.Boaz Tsaban & Lyubomyr Zdomskyy - 2006 - Journal of Symbolic Logic 71 (3):1053 - 1056.

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Citations of this work BETA

Selective Covering Properties of Product Spaces.Arnold W. Miller, Boaz Tsaban & Lyubomyr Zdomskyy - 2014 - Annals of Pure and Applied Logic 165 (5):1034-1057.
Products of Menger Spaces: A Combinatorial Approach.Piotr Szewczak & Boaz Tsaban - 2017 - Annals of Pure and Applied Logic 168 (1):1-18.
Guessing, Mind-Changing, and the Second Ambiguous Class.Samuel Alexander - 2016 - Notre Dame Journal of Formal Logic 57 (2):209-220.
Menger Remainders of Topological Groups.Angelo Bella, Seçil Tokgöz & Lyubomyr Zdomskyy - 2016 - Archive for Mathematical Logic 55 (5-6):767-784.

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