Type: Article

Restricted mad families

Guzmán, Osvaldo; Hrusak, Michael;

Abstract:

Let be an ideal on ?. By cov we denote the least size of a family such that for every infinite there is for which is infinite. We say that an AD family is a MAD family restricted to if for every infinite there is such that. Let a be the least size of an infinite MAD family restricted to. We prove that If {a,cov then a, and consequently, if is tall and then a {a,cov. We use these results to prove that if c then o and that as{a,non. We also analyze the problem whether it is consistent with the negation of CH that every AD family of size ?1 can be extended to a MAD family of size ?1. © 2019 The Association for Symbolic Logic.