The consistency strength of projective absoluteness

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


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



    Upload a copy of this work     Papers currently archived: 91,164

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.
Projective absoluteness for Sacks forcing.Daisuke Ikegami - 2009 - Archive for Mathematical Logic 48 (7):679-690.
The consistency strength of an infinitary Ramsey property.George Kafkoulis - 1994 - Journal of Symbolic Logic 59 (4):1158-1195.
Solovay models and forcing extensions.Joan Bagaria & Roger Bosch - 2004 - Journal of Symbolic Logic 69 (3):742-766.
Amoeba-absoluteness and projective measurability.Jörg Brendle - 1993 - Journal of Symbolic Logic 58 (4):1284-1290.
Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Projective prewellorderings vs projective wellfounded relations.Xianghui Shi - 2009 - Journal of Symbolic Logic 74 (2):579-596.
Projective spinor geometry and prespace.F. A. M. Frescura - 1988 - Foundations of Physics 18 (8):777-808.
Consistency strength of higher chang’s conjecture, without CH.Sean D. Cox - 2011 - Archive for Mathematical Logic 50 (7-8):759-775.
Bounded forcing axioms as principles of generic absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.
On the Consistency Strength of Two Choiceless Cardinal Patterns.Arthur W. Apter - 1999 - Notre Dame Journal of Formal Logic 40 (3):341-345.
A remark on the tree property in a choiceless context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.


Added to PP

38 (#397,063)

6 months
9 (#242,802)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A simple maximality principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
Projective Well-orderings of the Reals.Andrés Eduardo Caicedo & Ralf Schindler - 2006 - Archive for Mathematical Logic 45 (7):783-793.
Generic absoluteness.Joan Bagaria & Sy D. Friedman - 2001 - Annals of Pure and Applied Logic 108 (1-3):3-13.
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 12 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.
Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.

View all 15 references / Add more references