On the weak Freese-Nation property of complete Boolean algebras
| dc.creator | Fuchino, Sakaé | |
| dc.creator | Geschke, Stefan | |
| dc.creator | Shelah, Saharon | |
| dc.creator | Soukup, Lajos | |
| dc.date | 1999-11-28 | |
| dc.date.accessioned | 2026-07-07T05:31:59Z | |
| dc.date.available | 2026-07-07T05:31:59Z | |
| dc.description | The 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.identifier | https://arxiv.org/abs/math/9911230 | |
| dc.identifier | http://arxiv.org/abs/math/9911230 | |
| dc.identifier | Ann. Pure Appl. Logic 110 No. 1-3 (2001) 89--105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79502 | |
| dc.subject | Logic | |
| dc.title | On the weak Freese-Nation property of complete Boolean algebras | |
| dc.type | text |