Critical cardinalities and additivity properties of combinatorial notions of smallness

Abstract

Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (tau-covers). We deal with two types of combinatorial questions which arise from this study. 1. Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of the continuum. 2. We study the additivity numbers of the combinatorial notions corresponding to the topological diagonalization notions. This gives new insights on the structure of the eventual dominance ordering on the Baire space, the almost inclusion ordering on the Rothberger space, and the interactions between them.

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References in corpus (3)

• The combinatorics of Borel covers
• Additivity properties of topological diagonalizations
• Critical cardinalities and additivity properties of combinatorial notions of smallness

Cited by in corpus (9)

• Some new directions in infinite-combinatorial topology
• Additivity properties of topological diagonalizations
• Critical cardinalities and additivity properties of combinatorial notions of smallness
• The combinatorics of splittability
• Covering the Baire space by families which are not finitely dominating
• Selection Principles and special sets of reals: Open problems
• The combinatorics of tau-covers
• On the length of chains of proper subgroups covering a topological group
• A semifilter approach to selection principles II: tau*-covers