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Splitting, Bounding, and Almost Disjointness Can Be Quite Different

  Published:2016-07-19
 Printed: Jun 2017
  • Vera Fischer,
    Institut für Diskrete Mathematik und Geometrie, Technishe Universität Wien, Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria
  • Diego Alejandro Mejia,
    Institut für Diskrete Mathematik und Geometrie, Technishe Universität Wien, Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria
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Abstract

We prove the consistency of $$ \operatorname{add}(\mathcal{N})\lt \operatorname{cov}(\mathcal{N}) \lt \mathfrak{p}=\mathfrak{s} =\mathfrak{g}\lt \operatorname{add}(\mathcal{M}) = \operatorname{cof}(\mathcal{M}) \lt \mathfrak{a} =\mathfrak{r}=\operatorname{non}(\mathcal{N})=\mathfrak{c} $$ with $\mathrm{ZFC}$, where each of these cardinal invariants assume arbitrary uncountable regular values.
Keywords: cardinal characteristics of the continuum, splitting, bounding number, maximal almost-disjoint families, template forcing iterations, isomorphism-of-names cardinal characteristics of the continuum, splitting, bounding number, maximal almost-disjoint families, template forcing iterations, isomorphism-of-names
MSC Classifications: 03E17, 03E35, 03E40 show english descriptions Cardinal characteristics of the continuum
Consistency and independence results
Other aspects of forcing and Boolean-valued models
03E17 - Cardinal characteristics of the continuum
03E35 - Consistency and independence results
03E40 - Other aspects of forcing and Boolean-valued models
 

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