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Jensen's Σ* theory and the combinatorial content of V = L

Published online by Cambridge University Press:  12 March 2014

Sy D. Friedman
Sy D. Friedman*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, E-mail: [email protected]
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Extract

An awkward feature of the standard fine structure theory of the Jα's (see Jensen [72]) is that special parameters are required to make good sense of the notion of “Σn Skolem hull”, parameters which may not be preserved in condensation arguments.

The purpose of this article is to indicate how a reformulation of Jensen's Σ* theory (developed for the study of core models) can be used to provide a more satisfactory treatment of uniformization, hulls, and Skolem functions for the Jα's. Then we use this approach to fine structure to formulate a principle intended to capture the combinatorial content of the axiom V = L.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 1096 - 1104
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

Jensen, R. B. [72], The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.CrossRefGoogle Scholar
Jensen, R. B. [89], Handwritten notes on the Σ* theory.Google Scholar
Jensen, R. B. and Solovay, R. M. [68], Some applications of almost disjoint sets, Mathematical Logic and the Foundations of Set Theory (Bar-Hillel, Y.. editor), North-Holland, Amsterdam, 1970, pp. 84–104.Google Scholar