Brown, Elizabeth Theta; Groszek, Marcia J. Uncountable superperfect forcing and minimality. (English) Zbl 1110.03041 Ann. Pure Appl. Logic 144, No. 1-3, 73-82 (2006). 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. Cited in 5 Documents MSC: 03E40 Other aspects of forcing and Boolean-valued models 03E05 Other combinatorial set theory 03E35 Consistency and independence results Keywords:uncountable cardinals; tree forcing; minimality PDFBibTeX XMLCite \textit{E. T. Brown} and \textit{M. J. Groszek}, Ann. Pure Appl. Logic 144, No. 1--3, 73--82 (2006; Zbl 1110.03041) Full Text: DOI References: [1] Elizabeth Theta Brown, Superperfect forcing at uncountable cardinals (in press); Elizabeth Theta Brown, Superperfect forcing at uncountable cardinals (in press) [2] Cummings, James; Shelah, Saharon, Cardinal invariants above the continuum, Ann. Pure Appl. Logic, 75, 251-288 (1995) · Zbl 0835.03013 [3] Groszek, Marcia J., Combinatorics on ideals and forcing with trees, J. Symbolic Logic, 52, 582-593 (1987) · Zbl 0646.03048 [4] Kunen, Kenneth, Saturated ideals, J. Symbolic Logic, 43, 65-76 (1978) · Zbl 0395.03031 [5] Miller, Arnold W., Rational perfect set forcing, (Axiomatic Set Theory. Axiomatic Set Theory, Contemp. Math., vol. 31 (1984), Amer. Math. Soc.: Amer. Math. Soc. Providence RI), 143-159 · Zbl 0555.03020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.