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Splitting Families and Complete Separability

  Published:2013-09-30
 Printed: Mar 2014
  • Heike Mildenberger,
    Albert-Ludwigs-Universität, Freiburg
  • Dilip Raghavan,
    Kobe University
  • Juris Steprans,
    York University, Toronto, ON
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Abstract

We answer a question from Raghavan and Steprāns by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s} \leq \mathfrak{a}$, partially answering a question of Shelah.
Keywords: maximal almost disjoint family, cardinal invariants maximal almost disjoint family, cardinal invariants
MSC Classifications: 03E05, 03E17, 03E65 show english descriptions Other combinatorial set theory
Cardinal characteristics of the continuum
Other hypotheses and axioms
03E05 - Other combinatorial set theory
03E17 - Cardinal characteristics of the continuum
03E65 - Other hypotheses and axioms
 

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