A consistency result on thin-tall superatomic Boolean algebras

We prove that if [unk][unk] is an infinite cardinal with [unk]>[unk]=[unk]{[unk]^{ > [unk]}} = [unk], then there is a cardinal-preserving notion of forcing that forces the existence of a [unk][unk]-thin-tall superatomic Boolean algebra. Consistency for specific [unk][unk], like ω1{\omega _1},...

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Veröffentlicht in:	Proceedings of the American Mathematical Society 1992, Vol.115 (2), p.473-477
1. Verfasser:	MARTINEZ, J. C
Format:	Artikel
Sprache:	eng
Schlagworte:	Axioms Boolean algebras Cardinality Exact sciences and technology Logic and foundations Logical theorems Mathematical logic, foundations, set theory Mathematical set theory Mathematical theorems Mathematics Research article Sciences and techniques of general use Set theory Teoria de conjunts Urelements Àlgebra de Boole
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Beschreibung
Zusammenfassung:	We prove that if [unk][unk] is an infinite cardinal with [unk]>[unk]=[unk]{[unk]^{ > [unk]}} = [unk], then there is a cardinal-preserving notion of forcing that forces the existence of a [unk][unk]-thin-tall superatomic Boolean algebra. Consistency for specific [unk][unk], like ω1{\omega _1}, then follows as a corollary.
ISSN:	0002-9939 1088-6826 1088-6826
DOI:	10.1090/S0002-9939-1992-1079703-X