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Homogeneous almost disjoint families

✍ Scribed by Sharon Shelah; Juris Steprāns

Book ID
105129337
Publisher
Springer
Year
1994
Tongue
English
Weight
395 KB
Volume
31
Category
Article
ISSN
0002-5240

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Partitioner algebras are deÿned by Baumgartner and Weese (Trans. Amer. Math. Soc. 274 (2) (1982) 619) as a natural tool for studying the properties of maximal almost disjoint families of subsets of !. We prove from PFA + and ♦(S 2 0 ) that there exists a partitioner algebra which contains a subalgeb

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We show that it is consistent with ZFC + ¬CH that there is a maximal almost disjoint permutation family A ⊆ Sym(N) such that A is a proper subset of an eventually different family E ⊆ N N and |A| < |E|. We also ask several questions in this area.