On the non-existence of mad families

Haim Horowitz*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that the non-existence of mad families is equiconsistent with ZFC, answering an old question of Mathias. We also consider the above result in the general context of maximal independent sets in Borel graphs, and we construct a Borel graph G such that ZF+ DC+ “there is no maximal independent set in G” is equiconsistent with ZFC+ “there exists an inaccessible cardinal”.

Original languageEnglish
Pages (from-to)325-338
Number of pages14
JournalArchive for Mathematical Logic
Volume58
Issue number3-4
DOIs
StatePublished - 9 May 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • Amalgamation
  • Borel graphs
  • Forcing
  • Inaccessible cardinals
  • Mad families

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