On the weak Freese-Nation property of complete Boolean algebras

dc.creatorFuchino, Sakaé
dc.creatorGeschke, Stefan
dc.creatorShelah, Saharon
dc.creatorSoukup, Lajos
dc.date1999-11-28
dc.date.accessioned2026-07-07T05:31:59Z
dc.date.available2026-07-07T05:31:59Z
dc.descriptionThe following results are proved: (a) In a model obtained by adding aleph_2 Cohen reals, there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. (b) Modulo the consistency strength of a supercompact cardinal, the existence of a c.c.c. complete Boolean algebras without the weak Freese-Nation property consistent with GCH. (c) Under some consequences of the negation of 0^#, the weak Freese-Nation property of (P(omega),subseteq) is equivalent to the weak Freese-Nation property of any of C(kappa) or R(kappa) for uncountable kappa. (d) Modulo consistency of (aleph_{omega+1},aleph_omega)-->(aleph_1,aleph_0), it is consistent with GCH that the assertion in (c) does not hold and also that adding aleph_omega Cohen reals destroys the weak Freese-Nation property of (P(omega),subseteq)
dc.identifierhttps://arxiv.org/abs/math/9911230
dc.identifierhttp://arxiv.org/abs/math/9911230
dc.identifierAnn. Pure Appl. Logic 110 No. 1-3 (2001) 89--105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79502
dc.subjectLogic
dc.titleOn the weak Freese-Nation property of complete Boolean algebras
dc.typetext

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