Covering properties of \(\omega \)-mad families

  • Leandro Aurichi
  • Lyubomyr ZdomskyyEmail author


We prove that Martin’s Axiom implies the existence of a Cohen-indestructible mad family such that the Mathias forcing associated to its filter adds dominating reals, while \(\mathfrak b=\mathfrak c\) is consistent with the negation of this statement as witnessed by the Laver model for the consistency of Borel’s conjecture.


Menger space Mad family Cohen forcing Laver forcing 

Mathematics Subject Classification

Primary 03E35 54D20 Secondary 03E05 



The work reported here was carried out during the visit of the second named author at the Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, in July 2018. This visit was supported by FAPESP (2017/09252-3). The second named author thanks the first named author and Lucia Junqueira for their kind hospitality. In addition, we thank Osvaldo Guzman for his comments on the previous version of this paper. We are also grateful to the anonymous referee who among other things pointed out that our proof of Theorem 1.1 requires also the assumption \( cov ({\mathcal {N}})=\mathfrak c\).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São Paulo (ICMC-USP)São CarlosBrazil
  2. 2.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienViennaAustria

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