Strongly almost disjoint familes, revisited
Hajnal, A. ; Juhász, Istvan ; Shelah, Saharon
Fundamenta Mathematicae, Tome 163 (2000), p. 13-23 / Harvested from The Polish Digital Mathematics Library
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The relations M(κ,λ,μ) → B [resp. B(σ)] meaning that if A⊂[κ]λ with |A|=κ is μ-almost disjoint then A has property B [resp. has a σ-transversal] had been introduced and studied under GCH in [EH]. Our two main results here say the following: Assume GCH and let ϱ be any regular cardinal with a supercompact [resp. 2-huge] cardinal above ϱ. Then there is a ϱ-closed forcing P such that, in VP, we have both GCH and M(ϱ(+ϱ+1),ϱ+,ϱ)↛B [resp. M(ϱ(+ϱ+1),λ,ϱ)↛B(ϱ+) for all λ≤ϱ(+ϱ+1)]. These show that, consistently, the results of [EH] are sharp. The necessity of using large cardinals follows from the results of [Ko], [HJSh] and [BDJShSz].

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212425 
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     author = {A. Hajnal and Istvan Juh\'asz and Saharon Shelah},
     title = {Strongly almost disjoint familes, revisited},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {13-23},
     zbl = {0946.03057},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p13bwm}
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Hajnal, A.; Juhász, Istvan; Shelah, Saharon. Strongly almost disjoint familes, revisited. Fundamenta Mathematicae, Tome 163 (2000) pp. 13-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p13bwm/

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