✦ LIBER ✦

Adjoining Almost Disjoint Permutations

✍ Scribed by Yi Zhang

Book ID: 101371268
Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 131 KB
Volume: 48
Category: Article
ISSN: 0044-3050
DOI: 10.1002/1521-3870(200202)48:2<189::aid-malq189>3.0.co;2-g

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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The object of this paper is to study how many essentially different common transversals a family of convex sets on the plane can have. In particular we consider the case where the family consists of pairwise disjoint translates of a single convex set.