The largest countable inductive set is a mouse set

Journal of Symbolic Logic 64 (2):443-459 (1999)
Abstract
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)
Options
 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
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,018
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

8 ( #170,196 of 1,101,088 )

Recent downloads (6 months)

6 ( #44,461 of 1,101,088 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.