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Fine Structure and Iteration Trees
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the third publication in the Lecture Notes in Logic series, Mitchell and Steel construct an inner model with a Woodin cardinal and develop its fine structure theory. This work builds upon the existing theory of a model of the form L[E], where E is a coherent sequence of extenders, and relies upon the fine structure theory of L[E] models with strong cardinals, and the theory of iteration trees and 'backgrounded' L[E] models with Woodin cardinals. This work is what results when fine structure meets iteration trees.

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Dodd, A., Strong cardinals, unpublished notes.
Dodd, A. and Jensen, R. B., The core model, Annals of Math. Logic 20 (1981) 43-75.
Dodd, A. and Jensen, R. B., The Covering Lemma for K, Annals of Math. Logic 22 (1982), 1-30.
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Dodd, A. and Jensen, R. B., untitled notes on fine structure below a strong cardinal, unpublished.
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Mitchell, W., The core model for sequences of measures I, Math. Proc. of the Cambridge Phil. Soc. 95 (1984) 229-260.
Mitchell, W., The core model for sequences of measures II, to appear.
Martin, D. A. and Steel, J. R., Iteration trees, to appear.
Mitchell, W., Schimmerling, E., and Steel, J., The Covering Lemma up to One Woodin Cardinal, 1992, preprint.
Schimmerling, E., Combinatorial Principles in the Core Model for One Woodin cardinal, 1992, preprint.o
Steel, J. R., The Core Model Iterability Problem, in preparation.
Steel, J. R., Projectively Wellordered Inner Models, 1993, submitted to Annals of Pure and Applied Logic.
Steel, J. R., Inner Models with Many Woodin Cardinals, 1993, Annals of Pure and Applies Logic, to appear.


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