Geodesic
Strongs-Sequences and Variations on Martin's Axiom
Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 730-746

Voir la notice de l'article provenant de la source Cambridge University Press

As part of their study of βω — ω and βω 1 — ω 1, A. Szymanski and H. X. Zhou [3] were able to exploit the following difference between ω, and ω: ω 1, contains uncountably many disjoint sets whereas any uncountable family of subsets of ω is, at best, almost disjoint. To translate this distinction between ω1, and ω to a possible distinction between βω 1 — ω 1, and βω — ω they used the fact that if a pairwise disjoint family of sets and a subset of each member of is chosen then it is trivial to find a single set whose intersection with each member is the chosen set. However, they noticed, it is not clear that the same is true if is only a pairwise almost disjoint family even if we only require equality except on a finite set. But any homeomorphism from βω 1 — ω 1 to βω — ω would have to carry a disjoint family of subsets of ω 1, to an almost disjoint family of subsets of ω with this property. This observation should motivate the following definition. 
Steprāns, Juris. Strongs-Sequences and Variations on Martin's Axiom. Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 730-746. doi: 10.4153/CJM-1985-039-6
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[1] 1. Bell, M., Two Boolean algebras with extreme cellular and compactness properties, to appear in Can. J. Math. Google Scholar | DOI

[2] 2. Herink, C., Some applications of iterated forcing, Ph.D. dissertation, University of Wisconsin, Madison. Google Scholar

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[4] 4. Tall, F., Some applications of a generalized Martin's Axiom, to appear in Trans. A.M.S. Google Scholar

[5] 5. Weiss, W., Versions of Martin's Axiom, to appear in The Handbook of Set Theoretic Topology. Google Scholar

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