On the existence of strong chains in ℘(ω1)/Fin
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Abstract(Xα: α < ω2) ⊂ ℘(ω1) is a strong chain in ℘(ω1)/Fin if and only if Xβ – Xα is finite and Xα – Xβ is uncountable for each β < α < ω1. We show that it is consistent that a strong chain in ℘(ω1) exists. On the other hand we show that it is consistent that there is a strongly almost-disjoint family in ℘(ω1) but no strong chain exists: is used to construct a c.c.c forcing that adds a strong chain and Chang's Conjecture to prove that there is no strong chain.
1985 ◽
Vol 38
(2)
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pp. 198-206
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1985 ◽
Vol 37
(4)
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pp. 730-746
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1977 ◽
Vol 81
(3)
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pp. 523-523
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1987 ◽
Vol 101
(3)
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pp. 385-393
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1983 ◽
Vol 93
(1)
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pp. 1-7
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2012 ◽
Vol 64
(6)
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pp. 1378-1394
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