Critical cardinalities and additivity properties of combinatorial notions of smallness

S. Shelah, B. Tsaban

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (τ-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.

Original languageEnglish
Pages (from-to)149-162
Number of pages14
JournalJournal of Applied Analysis
Issue number2
StatePublished - Dec 2003

Bibliographical note

Funding Information:
2000 Mathematics Subject Classification. 03E17, 06A07, 03E35, 03E10. Key words and phrases. τ-cover, tower, splitting number, additivity number. The research of the first author is partially supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Publication 768. This paper constitutes a part of the second author’s doctoral dissertation at Bar-Ilan University.


  • Additivity number
  • Splitting number
  • Tower
  • τ-Cover


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