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Uncountable superperfect forcing and minimality. (English) Zbl 1110.03041

Summary: Uncountable superperfect forcing is tree forcing on regular uncountable cardinals \(\kappa\) with \(\kappa ^{<\kappa }=\kappa\), using trees in which the heights of nodes that split along any branch in the tree form a club set, and such that any node in the tree with more than one immediate extension has measure-one-many extensions, where the measure is relative to some \(\kappa\)-complete, nonprincipal normal filter (or p-filter) \(F\). This forcing adds a generic of minimal degree if and only if \(F\) is \(\kappa\)-saturated.

MSC:

03E40 Other aspects of forcing and Boolean-valued models
03E05 Other combinatorial set theory
03E35 Consistency and independence results
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References:

[1] Elizabeth Theta Brown, Superperfect forcing at uncountable cardinals (in press); Elizabeth Theta Brown, Superperfect forcing at uncountable cardinals (in press)
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