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Title: Forcing with ideals generated by closed sets (English)
Author: Zapletal, Jindřich
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 1
Year: 2002
Pages: 181-188
Category: math
Summary: Consider the poset $P_I=\text{\rm Borel}(\Bbb R)\setminus I$ where $I$ is an arbitrary $\sigma$-ideal $\sigma$-generated by a projective collection of closed sets. Then the $P_I$ extension is given by a single real $r$ of an almost minimal degree: every real $s\in V[r]$ is Cohen-generic over $V$ or $V[s]=V[r]$. (English)
Keyword: forcing
Keyword: descriptive set theory
Keyword: large cardinals
MSC: 03E15
MSC: 03E17
MSC: 03E40
MSC: 03E55
MSC: 03E60
idZBL: Zbl 1069.03037
idMR: MR1903318
Date available: 2009-01-08T19:20:58Z
Last updated: 2012-04-30
Stable URL:
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Reference: [N] Neeman I., Zapletal J.: Proper forcings and absoluteness in $L(\Bbb R)$.Comment. Math. Univ. Carolinae (1998), 39 281-301. Zbl 0939.03054, MR 1651950
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Reference: [Z1] Zapletal J.: Isolating cardinal invariants.J. Math. Logic accepted. Zbl 1025.03046
Reference: [Z2] Zapletal J.: Countable support iteration revisited.J. Math. Logic submitted.


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