MAD families with strong combinatorial properties

Volume 193 / 2007

Jörg Brendle, Greg Piper Fundamenta Mathematicae 193 (2007), 7-21 MSC: Primary 03E50; Secondary 03E05, 03E15, 03E40. DOI: 10.4064/fm193-1-2

Abstract

In his paper in Fund. Math. 178 (2003), Miller presented two conjectures regarding MAD families. The first is that CH implies the existence of a MAD family that is also a $\sigma $-set. The second is that under CH, there is a MAD family concentrated on a countable subset. These are proved in the present paper.

Authors

  • Jörg BrendleThe Graduate School of Science and Technology
    Kobe University
    Rokko-dai 1-1, Nada-ku
    Kobe 657-8501, Japan
    e-mail
  • Greg PiperThe Graduate School of Science and Technology
    Kobe University
    Rokko-dai 1-1, Nada-ku
    Kobe 657-8501, Japan
    e-mail

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