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Patterns of projecta1

Published online by Cambridge University Press:  12 March 2014

Adam Krawczyk
Adam Krawczyk*
Affiliation:
University of Warsaw, 00-901 Warsaw, Pkin IXP, Poland
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Abstract

Roughly speaking, a pattern is a finite sequence coding the set of natural numbers n for which the Σn+1 projectum is less than the Σn projectum for a given admissible ordinal. We prove that for each pattern there exists an ordinal realizing it. Several results on the orderings of patterns are given. We conclude the paper with remarks on Δn projecta. The main technique, used throughout the paper, is Jensen's Uniformisation Theorem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 2 , June 1981 , pp. 287 - 295
Copyright
Copyright © Association for Symbolic Logic 1981

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Footnotes

1

This paper contains one chapter of the author's doctoral dissertation. I would like to express my gratitude to my advisor Professor Wiktor Marek for many illuminating discussions and specially for suggesting the subject.

References

REFERENCES

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[3]Devlin, K. J., Aspects of constructibility, Lecture Notes in Mathematics, no. 354, Springer-Verlag, Berlin and New York, 1973.Google Scholar
[4]Jensen, R. B., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.CrossRefGoogle Scholar
[5]Simpson, S. G., Short course on admissible recursion theory, Second Symposium on Generalized Recursion Theory, North-Holland, Amsterdam, 1978.Google Scholar