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Combinatorial images of sets of reals and semifilter trichotomy
Published online by Cambridge University Press: 12 March 2014
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.
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- Copyright © Association for Symbolic Logic 2008
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