Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/14658
DC Field | Value | Language |
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dc.contributor.author | Kurilić, Miloš | en |
dc.date.accessioned | 2020-03-03T14:56:54Z | - |
dc.date.available | 2020-03-03T14:56:54Z | - |
dc.date.issued | 2007-03-01 | en |
dc.identifier.issn | 01680072 | en |
dc.identifier.uri | https://open.uns.ac.rs/handle/123456789/14658 | - |
dc.description.abstract | According to [M.S. Kurilić, Cohen-stable families of subsets of the integers, J. Symbolic Logic 66 (1) (2001) 257-270], adding a Cohen real destroys a splitting family S on ω if and only if S is isomorphic to a splitting family on the set of rationals, Q, whose elements have nowhere dense boundaries. Consequently, | S | < cov (M) implies the Cohen-indestructibility of S. Using the methods developed in [J. Brendle, S. Yatabe, Forcing indestructibility of MAD families, Ann. Pure Appl. Logic 132 (2-3) (2005) 271-312] the stability of splitting families in several forcing extensions is characterized in a similar way (roughly speaking, destructible families have members with 'small generalized boundaries' in the space of the reals). Also, it is proved that a splitting family is preserved by the Sacks (respectively: Miller, Laver) forcing if and only if it is preserved by some forcing which adds a new (respectively: an unbounded, a dominating) real. The corresponding hierarchy of splitting families is investigated. © 2006 Elsevier B.V. All rights reserved. | en |
dc.relation.ispartof | Annals of Pure and Applied Logic | en |
dc.title | Splitting families and forcing | en |
dc.type | Journal/Magazine Article | en |
dc.identifier.doi | 10.1016/j.apal.2006.08.002 | en |
dc.identifier.scopus | 2-s2.0-33845954280 | en |
dc.identifier.url | https://api.elsevier.com/content/abstract/scopus_id/33845954280 | en |
dc.relation.lastpage | 251 | en |
dc.relation.firstpage | 240 | en |
dc.relation.issue | 3 | en |
dc.relation.volume | 145 | en |
item.fulltext | No Fulltext | - |
item.grantfulltext | none | - |
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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