Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/16087
DC Field | Value | Language |
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dc.contributor.author | Kurilić, Miloš | en |
dc.contributor.author | Pavlović A. | en |
dc.date.accessioned | 2020-03-03T15:02:32Z | - |
dc.date.available | 2020-03-03T15:02:32Z | - |
dc.date.issued | 2007-09-01 | en |
dc.identifier.issn | 01680072 | en |
dc.identifier.uri | https://open.uns.ac.rs/handle/123456789/16087 | - |
dc.description.abstract | A sequence x = 〈 xn : n ∈ ω 〉 of elements of a complete Boolean algebra (briefly c.B.a.) B converges to b ∈ B a priori (in notation x → b) if lim inf x = lim sup x = b. The sequential topology τs on B is the maximal topology on B such that x → b implies x →τs b, where →τs denotes the convergence in the space 〈 B, τs 〉 - the a posteriori convergence. These two forms of convergence, as well as the properties of the sequential topology related to forcing, are investigated. So, the a posteriori convergence is described in terms of killing of tall ideals on ω, and it is shown that the a posteriori convergence is equivalent to the a priori convergence iff forcing by B does not produce new reals. A property (h{stroke}) of c.B.a.'s, satisfying t-cc ⇒ (h{stroke}) ⇒ s-cc and providing an explicit (algebraic) definition of the a posteriori convergence, is isolated. Finally, it is shown that, for an arbitrary c.B.a. B, the space 〈 B, τs 〉 is sequentially compact iff the algebra B has the property (h{stroke}) and does not produce independent reals by forcing, and that s = ω1 implies P (ω) is the unique sequentially compact c.B.a. in the class of Suslin forcing notions. © 2007 Elsevier B.V. All rights reserved. | en |
dc.relation.ispartof | Annals of Pure and Applied Logic | en |
dc.title | A posteriori convergence in complete Boolean algebras with the sequential topology | en |
dc.type | Journal/Magazine Article | en |
dc.identifier.doi | 10.1016/j.apal.2007.05.002 | en |
dc.identifier.scopus | 2-s2.0-34548421872 | en |
dc.identifier.url | https://api.elsevier.com/content/abstract/scopus_id/34548421872 | en |
dc.relation.lastpage | 62 | en |
dc.relation.firstpage | 49 | en |
dc.relation.issue | 1-3 | en |
dc.relation.volume | 148 | en |
item.grantfulltext | none | - |
item.fulltext | No Fulltext | - |
crisitem.author.dept | Prirodno-matematički fakultet, Departman za matematiku i informatiku | - |
crisitem.author.parentorg | Prirodno-matematički fakultet | - |
Appears in Collections: | PMF Publikacije/Publications |
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