Comparing the closed almost disjointness and dominating numbers

Volume 217 / 2012

Dilip Raghavan, Saharon Shelah Fundamenta Mathematicae 217 (2012), 73-81 MSC: 03E35, 03E65, 03E17, 03E05. DOI: 10.4064/fm217-1-6


We prove that if there is a dominating family of size $\aleph _{1}$, then there are $\aleph _{1}$ many compact subsets of $\omega ^{\omega }$ whose union is a maximal almost disjoint family of functions that is also maximal with respect to infinite partial functions.


  • Dilip RaghavanGraduate School of System Informatics
    Kobe University
    Kobe 657-8501, Japan
  • Saharon ShelahInstitute of Mathematics
    The Hebrew University
    Jerusalem, Israel
    Department of Mathematics
    Rutgers University
    Piscataway, NJ 08854, U.S.A.

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