The largest countable inductive set is a mouse set

Journal of Symbolic Logic 64 (2):443-459 (1999)
Let κ R be the least ordinal κ such that L κ (R) is admissible. Let $A = \{x \in \mathbb{R} \mid (\exists\alpha such that x is ordinal definable in L α (R)}. It is well known that (assuming determinacy) A is the largest countable inductive set of reals. Let T be the theory: ZFC - Replacement + "There exists ω Woodin cardinals which are cofinal in the ordinals." T has consistency strength weaker than that of the theory ZFC + "There exists ω Woodin cardinals", but stronger than that of the theory ZFC + "There exists n Woodin Cardinals", for each n ∈ ω. Let M be the canonical, minimal inner model for the theory T. In this paper we show that A = R ∩ M. Since M is a mouse, we say that A is a mouse set. As an application, we use our characterization of A to give an inner-model-theoretic proof of a theorem of Martin which states that for all n, every Σ * n real is in A
Keywords Large Cardinals   Descriptive Set Theory   Inner Model Theory
Categories (categorize this paper)
DOI 10.2307/2586477
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,188
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
The Envelope of a Pointclass Under a Local Determinacy Hypothesis.Trevor M. Wilson - 2015 - Annals of Pure and Applied Logic 166 (10):991-1018.

Add more citations

Similar books and articles
A Model with No Magic Set.Krzysztof Ciesielski & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (4):1467-1490.
Elementary Extensions of Countable Models of Set Theory.John E. Hutchinson - 1976 - Journal of Symbolic Logic 41 (1):139-145.
Proper Forcing and L(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
Consequences of Arithmetic for Set Theory.Lorenz Halbeisen & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):30-40.
Iterates of the Core Model.Ralf Schindler - 2006 - Journal of Symbolic Logic 71 (1):241 - 251.
Locally Countable Models of Σ1-Separation.Fred G. Abramson - 1981 - Journal of Symbolic Logic 46 (1):96 - 100.
Order Types of Ordinals in Models of Set Theory.John E. Hutchinson - 1976 - Journal of Symbolic Logic 41 (2):489-502.

Monthly downloads

Added to index


Total downloads

159 ( #28,223 of 2,153,857 )

Recent downloads (6 months)

1 ( #398,274 of 2,153,857 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums