The consistency strength of projective absoluteness

Annals of Pure and Applied Logic 74 (3):245-295 (1995)
  Copy   BIBTEX

Abstract

It is proved that in the absence of proper class inner models with Woodin cardinals, for each n ε {1,…,ω}, ∑3 + n1 absoluteness implies there are n strong cardinals in K (where this denotes a suitably defined global version of the core model for one Woodin cardinal as exposed by Steel. Combined with a forcing argument of Woodin, this establishes that the consistency strength of ∑3 + n1 absoluteness is exactly that of n strong cardinals so that in particular projective absoluteness is equiconsistent with the existence of infinitely many strong cardinals. It is also argued how this theorem is to be construed as the first step in the long range program of showing that projective determinacy is equivalent to its analytical consequences for the projective sets which would settle positively a conjecture of Woodin and thereby solve the last Delfino problem

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,505

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

Proper forcing extensions and Solovay models.Joan Bagaria & Roger Bosch - 2004 - Archive for Mathematical Logic 43 (6):739-750.
The core model for almost linear iterations.Ralf-Dieter Schindler - 2002 - Annals of Pure and Applied Logic 116 (1-3):205-272.
Inner models in the region of a Woodin limit of Woodin cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
Projective Well-orderings of the Reals.Andrés Eduardo Caicedo & Ralf Schindler - 2006 - Archive for Mathematical Logic 45 (7):783-793.
Easton’s theorem in the presence of Woodin cardinals.Brent Cody - 2013 - Archive for Mathematical Logic 52 (5-6):569-591.
Core Models in the Presence of Woodin Cardinals.Ralf Schindler - 2006 - Journal of Symbolic Logic 71 (4):1145 - 1154.
Elementary chains and C (n)-cardinals.Konstantinos Tsaprounis - 2014 - Archive for Mathematical Logic 53 (1-2):89-118.

Analytics

Added to PP
2014-01-16

Downloads
52 (#419,921)

6 months
7 (#718,806)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A simple maximality principle.Joel Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
Generic absoluteness.Joan Bagaria & Sy D. Friedman - 2001 - Annals of Pure and Applied Logic 108 (1-3):3-13.
Projective Well-orderings of the Reals.Andrés Eduardo Caicedo & Ralf Schindler - 2006 - Archive for Mathematical Logic 45 (7):783-793.
Projective uniformization revisited.Kai Hauser & Ralf-Dieter Schindler - 2000 - Annals of Pure and Applied Logic 103 (1-3):109-153.
Strong cardinals in the core model.Kai Hauser & Greg Hjorth - 1997 - Annals of Pure and Applied Logic 83 (2):165-198.

View all 13 citations / Add more citations

References found in this work

The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory.Kurt Gödel - 1940 - Princeton university press;: Princeton University Press;. Edited by George William Brown.
The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
The Independence of the Continuum Hypothesis.Paul J. Cohen - 1963 - Proceedings of the National Academy of Sciences of the United States of America 50 (6):1143--8.
The Independence of the Continuum Hypothesis II.Paul Cohen - 1964 - Proc. Nat. Acad. Sci. USA 51 (1):105-110.
Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.

View all 14 references / Add more references