On non-wellfounded iterations of the perfect set forcing

Journal of Symbolic Logic 64 (2):551-574 (1999)

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Abstract
We prove that if I is a partially ordered set in a countable transitive model M of ZFC then M can be extended by a generic sequence of reals a i , i ∈ I, such that ℵ M 1 is preserved and every a i is Sacks generic over $\mathfrak{M}[\langle \mathbf{a}_j: j . The structure of the degrees of M-constructibility of reals in the extension is investigated. As applications of the methods involved, we define a cardinal invariant to distinguish product and iterated Sacks extensions, and give a short proof of a theorem (by Budinas) that in ω 2 -iterated Sacks extension of L the Burgess selection principle for analytic equivalence relations holds
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DOI 10.2307/2586484
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References found in this work BETA

Iterated Perfect-Set Forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
Applications of Iterated Perfect Set Forcing.Marcia J. Groszek - 1988 - Annals of Pure and Applied Logic 39 (1):19-53.
Iterated Perfectset Forcing.J. E. Baumgartner - 1979 - Annals of Mathematical Logic 17 (3):271.

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Citations of this work BETA

Forcing Indestructibility of MAD Families.Jörg Brendle & Shunsuke Yatabe - 2005 - Annals of Pure and Applied Logic 132 (2):271-312.
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On Coding Uncountable Sets by Reals.Joan Bagaria & Vladimir Kanovei - 2010 - Mathematical Logic Quarterly 56 (4):409-424.
Inner Mantles and Iterated HOD.Jonas Reitz & Kameryn J. Williams - 2019 - Mathematical Logic Quarterly 65 (4):498-510.

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