More about λ-support iterations of (<λ)-complete forcing notions

&
Archive for Mathematical Logic 52 (5-6):603-629 (2013)
  Copy   BIBTEX

Abstract

This article continues Rosłanowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) and we introduce here a new property of (<λ)-strategically complete forcing notions which implies that their λ-support iterations do not collapse λ + (for a strongly inaccessible cardinal λ)

Categories

Keywords

Reprint years

DOI

10.1007/s00153-013-0334-y

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

External links

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

Through your library

My notes

Similar books and articles

Reasonable Ultrafilters, Again.Andrzej Rosłanowski & Saharon Shelah - 2011 - Notre Dame Journal of Formal Logic 52 (2):113-147.
Simplified RCS iterations.Chaz Schlindwein - 1993 - Archive for Mathematical Logic 32 (5):341-349.
Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Unfoldable cardinals and the GCH.Joel David Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.
Sweet & sour and other flavours of ccc forcing notions.Andrzej Rosłanowski & Saharon Shelah - 2004 - Archive for Mathematical Logic 43 (5):583-663.
Strongly unfoldable cardinals made indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.
Proper forcing extensions and Solovay models.Joan Bagaria & Roger Bosch - 2004 - Archive for Mathematical Logic 43 (6):739-750.
Universal forcing notions and ideals.Andrzej Rosłanowski & Saharon Shelah - 2007 - Archive for Mathematical Logic 46 (3-4):179-196.
Distributive proper forcing axiom and cardinal invariants.Huiling Zhu - 2013 - Archive for Mathematical Logic 52 (5-6):497-506.
N–localization property.Andrzej Rosłanowski - 2006 - Journal of Symbolic Logic 71 (3):881 - 902.
More forcing notions imply diamond.Andrzej Rosłanowski & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):299-313.
Simple forcing notions and forcing axioms.Andrzej Rosłanowski & Saharon Shelah - 1997 - Journal of Symbolic Logic 62 (4):1297-1314.
Sacks forcing, Laver forcing, and Martin's axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
▵1 3-Stability.Dror Ben-Arié & Haim Judah - 1993 - Journal of Symbolic Logic 58 (3):941 - 954.

Analytics

Added to PP
2013-11-23

Downloads
34 (#456,993)

6 months
4 (#818,853)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
Higher Miller forcing may collapse cardinals.Heike Mildenberger & Saharon Shelah - 2021 - Journal of Symbolic Logic 86 (4):1721-1744.
A parallel to the null ideal for inaccessible $$\lambda $$ λ : Part I.Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (3-4):319-383.

Add more citations

References found in this work

Perfect-set forcing for uncountable cardinals.Akihiro Kanamori - 1980 - Annals of Mathematical Logic 19 (1-2):97-114.
Fusion and large cardinal preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.
Reasonable Ultrafilters, Again.Andrzej Rosłanowski & Saharon Shelah - 2011 - Notre Dame Journal of Formal Logic 52 (2):113-147.
Uncountable superperfect forcing and minimality.Elizabeth Theta Brown & Marcia J. Groszek - 2006 - Annals of Pure and Applied Logic 144 (1-3):73-82.

Add more references