We prove covering theorems for K, where K is the core model below the sharp for a strong cardinal, and give an application to stationary set reflection

Annals of Pure and Applied Logic 161 (1):94-108 (2010)
  Copy   BIBTEX

Abstract

We present several forcing posets for adding a non-reflecting stationary subset of Pω1, where λ≥ω2. We prove that PFA is consistent with dense non-reflection in Pω1, which means that every stationary subset of Pω1 contains a stationary subset which does not reflect to any set of size 1. If λ is singular with countable cofinality, then dense non-reflection in Pω1 follows from the existence of squares

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,509

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

Full Reflection at a Measurable Cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.
Club-Guessing, Stationary Reflection, and Coloring Theorems.Todd Eisworth - 2010 - Annals of Pure and Applied Logic 161 (10):1216-1243.
Local Saturation of the Non-Stationary Ideal Over Pκλ.Toshimichi Usuba - 2007 - Annals of Pure and Applied Logic 149 (1-3):100-123.
Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Simultaneous Reflection and Impossible Ideals.Todd Eisworth - 2012 - Journal of Symbolic Logic 77 (4):1325-1338.
Stationary Cardinals.Wenzhi Sun - 1993 - Archive for Mathematical Logic 32 (6):429-442.
Splitting Stationary Sets In.Toshimichi Usuba - 2012 - Journal of Symbolic Logic 77 (1):49-62.
Semistationary and Stationary Reflection.Hiroshi Sakai - 2008 - Journal of Symbolic Logic 73 (1):181-192.
Nonsplitting Subset of $Mathscr{P}_kappa(Kappa^+)$.Moti Gitik - 1985 - Journal of Symbolic Logic 50 (4):881-894.

Analytics

Added to PP
2015-02-05

Downloads
0

6 months
0

Historical graph of downloads

Sorry, there are not enough data points to plot this chart.
How can I increase my downloads?

Author's Profile

David Aspero
University of East Anglia

Citations of this work

Operations, Climbability and the Proper Forcing Axiom.Yasuo Yoshinobu - 2013 - Annals of Pure and Applied Logic 164 (7-8):749-762.
Forcing Axioms, Approachability, and Stationary Set Reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.

Add more citations

References found in this work

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Combinatorial Principles in the Core Model for One Woodin Cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
A Very Weak Square Principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.

View all 8 references / Add more references