The fine structure of real mice

Journal of Symbolic Logic 63 (3):937-994 (1998)
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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 + ¬ DC R



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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.
The real core model and its scales.Daniel W. Cunningham - 1995 - Annals of Pure and Applied Logic 72 (3):213-289.
Is there a set of reals not in K(R)?Daniel W. Cunningham - 1998 - Annals of Pure and Applied Logic 92 (2):161-210.

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