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Extenders, embedding normal forms, and the Martin-Steel-theorem

Published online by Cambridge University Press:  12 March 2014

Peter Koepke*
Affiliation:
Mathematisches Institut, Beringstrasse 4, D-53115 Bonn, Germany E-mail: koepke@math.uni-bonn.de

Abstract

We propose a simple notion of “extender” for coding large elementary embeddings of models of set theory. As an application we present a self-contained proof of the theorem by D. Martin and J. Steel that infinitely many Woodin cardinals imply the determinacy of every projective set.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1]Devlin, K. J. and Jensen, R. B., Marginalia to a theorem of Silver, ⊨ ISILC logic conference, Lecture Notes in Mathematics, no. 499, Springer-Verlag, Berlin and New York, 1975, pp. 115142.CrossRefGoogle Scholar
[2]Dodd, A., The core model, Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
[3]Drake, F. R., Set theory: An introduction to large cardinals, North-Holland, Amsterdam, 1974.Google Scholar
[4]Friedman, S. D., Embedding hierarchies, unpublished notes.Google Scholar
[5]Gale, D. and Stewart, F. M., Infinite games with perfect information, Annals of Mathematics Studies, vol. 28 (1953), pp. 245266.Google Scholar
[6]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[7]Kechris, A. S., Classical descriptive set theory, Springer-Verlag, Berlin and New York, 1995.CrossRefGoogle Scholar
[8]Koepke, P., An introduction to extenders and core models for extender sequences, Logic colloquium 1987, North-Holland, Amsterdam, 1989, pp. 137182.Google Scholar
[9]Martin, D. A., Measurable cardinals and analytic games, Fundamenta Mathematicae, vol. 66 (1970), pp. 287291.Google Scholar
[10]Martin, D. A. and Steel, J. R., A proof of projective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), pp. 71125.CrossRefGoogle Scholar
[11]Martin, D. A. and Steel, J. R., Iteration trees, Journal of the American Mathematical Society, vol. 7 (1994), pp. 173.CrossRefGoogle Scholar
[12]Mitchell, W. J., Hypermeasurable cardinals, Logic colloquium 1978, North-Holland, Amsterdam, 1979, pp. 303316.Google Scholar
[13]Moschovakis, Y. N., Descriptive set theory, North-Holland, Amsterdam, 1980.Google Scholar
[14]Windßus, K., Projektive Determiniertheit, Diplomarbeit, Bonn, 1993.Google Scholar