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GENERIC EXISTENCE OF MAD FAMILIES

  • OSVALDO GUZMÁN-GONZÁLEZ (a1), MICHAEL HRUŠÁK (a2), CARLOS AZAREL MARTÍNEZ-RANERO (a3) and ULISES ARIET RAMOS-GARCÍA (a4)

Abstract

In this note we study generic existence of maximal almost disjoint (MAD) families. Among other results we prove that Cohen-indestructible families exist generically if and only if b = c. We obtain analogous results for other combinatorial properties of MAD families, including Sacks-indestructibility and being +-Ramsey.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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