Combinatorial images of sets of reals and semifilter trichotomy

Details Combinatorial images of sets of reals and semifilter trichotomy Combinatorial images of sets of reals and semifilter trichotomy

2006-04-25

arxiv.org/abs/math/0604536v3

Journal of Symbolic Logic 73 (2008), 1278-1288

Mathematics

Logic

Small updates

Scientific paper

10.2178/jsl/1230396918

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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