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On non-wellfounded iterations of the perfect set forcing

Published online by Cambridge University Press:  12 March 2014

Vladimir Kanovei
Vladimir Kanovei*
Affiliation:
Moscow Center of Continuous Mathematical Education, Bolshaya Cherkizovskaya St, 9, Kor. 4 KV. 94, Moscow 107392, Russia E-mail: [email protected], [email protected]
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Abstract

We prove that if I is a partially ordered set in a countable transitive model of ZFC then can be extended by a generic sequence of reals ai, i ∈ I, such that is preserved and every ai is Sacks generic over [〈aj: j < i〉]. The structure of the degrees of -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 ω2-iterated Sacks extension of L the Burgess selection principle for analytic equivalence relations holds.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 551 - 574
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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