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A weak Dodd-Jensen lemma

Published online by Cambridge University Press:  12 March 2014

Itay Neeman  and
John Steel
Itay Neeman
Affiliation:
Harvard University, Department of Mathematics, 1 Oxford St. Cambridge, MA 02138, E-mail: ineeman@math.harvard.edu
John Steel
Affiliation:
University of California-Berkeley, Department of Mathematics, Berkeley, CA 94720-3840, E-mail: steel@math.berkeley.edu
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Abstract

We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1285 - 1294
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1] Martin, D.A. and Steel, J. R., Iteration trees, Journal of the American Mathematical Society, vol. 7 (1994), pp. 1–73.Google Scholar
[2] Mitchell, W.J. and Steel, J.R., Fine structure and iteration trees, Lecture Notes in Logic, vol. 3, Springer-Verlag, 1994.Google Scholar
[3] Schimmerling, E. and Steel, J.R., Fine structure for tame inner models, this Journal, vol. 61 (1996), pp. 621–639.Google Scholar
[4] Steel, J.R., Inner models with many Woodin cardinals, Annals of Pure and Applied Logic, vol. 65 (1993), pp. 185–209.Google Scholar
[5] Steel, J.R., The Core Model iterability problem, Lecture Notes in Logic, vol. 8, Spinger-Verlag, 1996.Google Scholar