A forcing construction of thin-tall Boolean algebras
Martínez, Juan
Fundamenta Mathematicae, Tome 159 (1999), p. 99-113 / Harvested from The Polish Digital Mathematics Library
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It was proved by Juhász and Weiss that for every ordinal α with 0<α<ω2 there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that κ<κ=κ and α is an ordinal such that 0<α<κ++, then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all α<κ++, we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic extension there is a superatomic Boolean algebra of height α and width κ for every α<κ++. Consistency for specific κ, like ω1, then follows as a corollary.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212328 
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     year = {1999},
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Martínez, Juan. A forcing construction of thin-tall Boolean algebras. Fundamenta Mathematicae, Tome 159 (1999) pp. 99-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv159i2p99bwm/

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