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arXiv · math/0604536

Combinatorial images of sets of reals and semifilter trichotomy

Boaz Tsaban·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 weaker form of this problem.

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BibTeXRIS

Boaz Tsaban, Lyubomyr Zdomskyy. 2006-04-25. Combinatorial images of sets of reals and semifilter trichotomy. https://doi.org/10.2178/jsl/1230396918

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