A Characterization of Generalized Příkrý Sequences

Archive for Mathematical Logic 44 (8):935-971 (2005)
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A generalization of Příkrý's forcing is analyzed which adjoins to a model of ZFC a set of order type at most ω below each member of a discrete set of measurable cardinals. A characterization of generalized Příkrý generic sequences reminiscent of Mathias' criterion for Příkrý genericity is provided, together with a maximality theorem which states that a generalized Příkrý sequence almost contains every other one lying in the same extension.This forcing can be used to falsify the covering lemma for a higher core model if there is an inner model with infinitely many measurable cardinals – changing neither cardinalities nor cofinalities. Another application is an alternative proof of a theorem of Mitchell stating that if the core model contains a regular limit θ of measurable cardinals, then there is a model in which every set of measurable cardinals of K bounded in θ has an indiscernible sequence but there is no such sequence for the entire set of measurables of K below θ



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Citations of this work

On sequences generic in the sense of Magidor.Gunter Fuchs - 2014 - Journal of Symbolic Logic 79 (4):1286-1314.
A Mathias criterion for the Magidor iteration of Prikry forcings.Omer Ben-Neria - 2023 - Archive for Mathematical Logic 63 (1):119-134.
Countable Length Everywhere Club Uniformization.William Chan, Stephen Jackson & Nam Trang - 2023 - Journal of Symbolic Logic 88 (4):1556-1572.

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References found in this work

The covering lemma for L[U].A. J. Dodd & R. B. Jensen - 1982 - Annals of Mathematical Logic 22 (2):127-135.
The covering lemma for L[U].A. J. Dodd - 1982 - Annals of Mathematical Logic 22 (2):127.

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