Combinatorial images of sets of reals and semifilter trichotomy

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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References in corpus (7)

• Scales, fields, and a problem of Hurewicz
• A semifilter approach to selection principles
• Additivity numbers of covering properties
• Partition relations for Hurewicz-type selection hypotheses
• Covering the Baire space by families which are not finitely dominating
• A remark on Fremlin-Miller theorem concerning the Menger property and Michael concentrated sets
• Menger's covering property and groupwise density

Cited by in corpus (7)

• Products of Menger spaces: a combinatorial approach
• Selective covering properties of product spaces
• Lindelof spaces which are indestructible, productive, or D
• On Guessing Whether A Sequence Has A Certain Property
• On localization of the Menger property
• Lindelof indestructibility, topological games and selection principles
• Guessing, Mind-changing, and the Second Ambiguous Class