On Weakly Tight Families
2012 ◽
Vol 64
(6)
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pp. 1378-1394
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Keyword(s):
Abstract Using ideas from Shelah's recent proof that a completely separable maximal almost disjoint family exists when 𝔠 < ℵω, we construct a weakly tight family under the hypothesis 𝔰 ≤ 𝔟 < ℵω. The case when 𝔰 < 𝔟 is handled in ZFC and does not require 𝔟 < ℵω, while an additional PCF type hypothesis, which holds when 𝔟 < ℵω is used to treat the case 𝔰 = 𝔟. The notion of a weakly tight family is a natural weakening of the well-studied notion of a Cohen indestructible maximal almost disjoint family. It was introduced by Hrušák and García Ferreira [8], who applied it to the Katétov order on almost disjoint families.
1983 ◽
Vol 93
(1)
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pp. 1-7
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Keyword(s):
2014 ◽
Vol 57
(1)
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pp. 119-124
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2002 ◽
Vol 117
(1-3)
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pp. 223-259
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1985 ◽
Vol 38
(2)
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pp. 198-206
Keyword(s):
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