A Characterization of Generalized Příkrý Sequences

Archive for Mathematical Logic 44 (8):935-971 (2005)
  Copy   BIBTEX

Abstract

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,271

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Generalized Prikry forcing and iteration of generic ultrapowers.Hiroshi Sakai - 2005 - Mathematical Logic Quarterly 51 (5):507-523.
Canonical seeds and Prikry trees.Joel David Hamkins - 1997 - Journal of Symbolic Logic 62 (2):373-396.
Supercompact extender based Prikry forcing.Carmi Merimovich - 2011 - Archive for Mathematical Logic 50 (5-6):591-602.
The consistency strength of choiceless failures of SCH.Arthur W. Apter & Peter Koepke - 2010 - Journal of Symbolic Logic 75 (3):1066-1080.
The short extenders gap two forcing is of Prikry type.Carmi Merimovich - 2009 - Archive for Mathematical Logic 48 (8):737-747.
Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
The short extenders gap three forcing using a morass.Carmi Merimovich - 2011 - Archive for Mathematical Logic 50 (1-2):115-135.
Iterated ultrapowers and prikry forcing.Patrick Dehornoy - 1978 - Annals of Mathematical Logic 15 (2):109-160.
On the strength of no normal precipitous filter.Moti Gitik & Liad Tal - 2011 - Archive for Mathematical Logic 50 (1-2):223-243.
Co-stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2006 - Journal of Symbolic Logic 71 (3):1029 - 1043.
On closed unbounded sets consisting of former regulars.Moti Gitik - 1999 - Journal of Symbolic Logic 64 (1):1-12.
Indestructible strong compactness and level by level inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.

Analytics

Added to PP
2013-11-23

Downloads
21 (#711,668)

6 months
6 (#506,019)

Historical graph of downloads
How can I increase my downloads?

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.

View all 7 citations / Add more citations

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.

Add more references