Uncountable superperfect forcing and minimality

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Annals of Pure and Applied Logic 144 (1-3):73-82 (2006)
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Abstract

Uncountable superperfect forcing is tree forcing on regular uncountable cardinals κ with κ<κ=κ, 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 κ-complete, nonprincipal normal filter F. This forcing adds a generic of minimal degree if and only if F is κ-saturated

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10.1016/j.apal.2006.05.012

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Citations of this work

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A Lifting Argument for the Generalized Grigorieff Forcing.Radek Honzík & Jonathan Verner - 2016 - Notre Dame Journal of Formal Logic 57 (2):221-231.
Perfect tree forcings for singular cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.

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References found in this work

Saturated ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Cardinal invariants above the continuum.James Cummings & Saharon Shelah - 1995 - Annals of Pure and Applied Logic 75 (3):251-268.
Combinatorics on ideals and forcing with trees.Marcia J. Groszek - 1987 - Journal of Symbolic Logic 52 (3):582-593.

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