Published online by Cambridge University Press: 12 March 2014
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.
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