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Israel Journal of Mathematics

, Volume 12, Issue 2, pp 207–214 | Cite as

Separability properties of almost — disjoint families of sets

  • Paul Erdös
  • Saharon Shelah
Article

Abstract

We solve here some problems arising from a work by Hechler [3]. We eliminate extra set-theoretic axioms (MA, in fact) from existence theorems and deal with the existence of disjoint sets.

Keywords

Acta Math Chromatic Number Separability Property Blue Point Infinite Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Erdös andA. Hajnal,On a property of families of sets, Acta Math. Acad. Sci. Hungar.12 (1961), 87–123.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    P. Erdös andA. Hajnal,On chromatic number of graphs and set systems, Acta Math. Acad. Sci. Hungar.17 (1966), 61.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. H. Hechler,Classifying a almost-disjoint families with applications to βN-N, Israel J. Math.10 (1971), 413–432.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    D. M. Martin andM. Solovay,Internal Cohen extensions, Annals of Math. Logic2 (1970), 143–178.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E. W. Miller,On a property of families of sets, Comptes Rendus Varsovie,30 (1937) 31–38.zbMATHGoogle Scholar
  6. 5.
    S. H. Hechler,Short complete nested sequences in βN-N and small almost-disjoint families, to appear in General Topology and its Appl.Google Scholar
  7. 7.
    P. Erdös,On a combinatorial problems II, Acta Math. Acad. Sci. Hungar.15 (1964), 445–447.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    W. M. Schmidt,Ein Kombinatorisches Problem von P. Erdös und A. Hajnal., Acta Math. Acad. Sci. Hungar.15 (1964), 373–374.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1972

Authors and Affiliations

  • Paul Erdös
    • 1
  • Saharon Shelah
    • 1
  1. 1.Technion-Israel Institute of TechnologyHaifa

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