2004/06/22 by Menahem Kojman, Wiesław Kubiś, Kojman, Menahem +4
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO
paper · pdf · doi:10.48550/arxiv.math/0406441
published as Proc. Amer. Math. Soc. 132 No. 11 (2004) 3357--3365
arxiv created 2004/06/22 · openalex publication_date 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an infinite cardinal mu, MAD(mu) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over mu. Erdos and Hechler proved the consistency of [mu in MAD(mu)] for a singular cardinal mu and asked if it was ever possible for a singular mu that [mu notin MAD(mu)], and also whether 2cf(mu) [mu in MAD(mu)] for every singular cardinal mu. We introduce a new method for controlling MAD(mu) for a singular mu and, among other new results about the structure of MAD(mu) for singular mu, settle both problems affirmatively.