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The fine structure of real mice

Published online by Cambridge University Press:  12 March 2014

Daniel W. Cunningham
Daniel W. Cunningham*
Affiliation:
Mathematics Department, State University of New York, College at Buffalo, Buffalo, NY 14222, USA E-mail: cunnindw@buffalostate.edu
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Abstract

Before one can construct scales of minimal complexity in the Real Core Model, K(ℝ), one needs to develop the fine-structure theory of K (ℝ). In this paper, the fine structure theory of mice, first introduced by Dodd and Jensen, is generalized to that of real mice. A relative criterion for mouse iterability is presented together with two theorems concerning the definability of this criterion. The proof of the first theorem requires only fine structure; whereas, the second theorem applies to real mice satisfying AD and follows from a general definability result obtained by abstracting work of John Steel on L(ℝ). In conclusion, we discuss several consequences of the work presented in this paper relevant to two issues: the complexity of scales in K(ℝ)and the strength of the theory ZF + AD + ┐DCℝ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 937 - 994
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

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