Combinatorial images of sets of reals and semifilter trichotomy
Logic
2010-11-02 v3 Combinatorics
General Topology
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 weaker form of this problem.
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Cite
@article{arxiv.math/0604536,
title = {Combinatorial images of sets of reals and semifilter trichotomy},
author = {Boaz Tsaban and Lyubomyr Zdomskyy},
journal= {arXiv preprint arXiv:math/0604536},
year = {2010}
}
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