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0# and inner models

Published online by Cambridge University Press:  12 March 2014

SY D. Friedman
SY D. Friedman*
Affiliation:
Institut für Formale Logik, Währinger Strasse 25, A-1090 Wien., Austria, E-mail: sdf@logic.univie.ac.at
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Extract

In this paper we examine the cardinal structure of inner models that satisfy GCH but do not contain 0#. We show, assuming that 0# exists, that such models necessarily contain Mahlo cardinals of high order, but without further assumptions need not contain a cardinal κ which is κ-Mahlo. The principal tools are the Covering Theorem for L and the technique of reverse Easton iteration.

Let I denote the class of Silver indiscernibles for L and 〈iα ∣ α ϵ ORD〉 its increasing enumeration. Also fix an inner model M of GCH not containing 0# and let ωα denote the ωα of the model M[0#], the least inner model containing M as a submodel and 0# as an element.

Keywords

Descriptive set theorylarge cardinalsinner models
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 924 - 932
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Devlin, K. and Jensen, R., Marginalia to a theorem of Silver, Lecture Notes, vol. 499, Springer, 1975, pp. 115–142.Google Scholar
[2]Friedman, S., Generic saturation, this Journal, vol. 63 (1998), pp. 158–162.Google Scholar