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Minimality in the Δ⅓-degrees

Published online by Cambridge University Press:  12 March 2014

Philip Welch*
Affiliation:
II Mathematische Institut, Freie Universität Berlin, 1000 Berlin 31, West Germany
*
School of Mathematics, University of Bristol, Bristol BS8 1TW, England

Abstract

We show in ZFC, assuming all reals have sharps, that a countable collection of Δ⅓-degrees without a minimal upper bound implies the existence of inner models with measurable cardinals.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCES

[CM]Dodd, A. J., The core model, London Mathematical Society Lecture Note Series, no. 61, Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
[F]Friedman, H., Minimality in the -degrees, Fundamenta Mathematicae, vol. 81 (1974), pp. 183192.CrossRefGoogle Scholar
[K]Kechris, A., Forcing with Δ perfect trees and minimal Δ-degrees, this Journal, vol. 46 (1981), pp. 803816.Google Scholar
[K2]Kechris, A., Minimal upper bounds for sequences of -degrees, this Journal, vol. 43 (1978), pp. 502507.Google Scholar
[K3]Kechris, A., Homogeneous trees and projective scales, Cabal seminar 77–79 (Kechris, A.et al., editors), Lecture Notes in Mathematics, vol. 839, Springer-Verlag, Berlin, 1981, pp. 3373.CrossRefGoogle Scholar
[Ko]Koepke, P., The theory of short core models, Ph.D. Thesis, University of Freiburg, Freiburg, 1983.Google Scholar
[Sa]Sacks, G., Forcing with perfect closed sets, Axiomatic set theory, Proceedings of Symposia in Pure Mathematics, vol. 13, part 1 (Scott, D., editor), American Mathematical Society, Providence, Rhode Island, 1971, pp. 331335.CrossRefGoogle Scholar
[Sa2]Sacks, G., Countable admissible ordinals and hyperdegrees, Advances in Mathematics, vol. 20 (1976), pp. 213262.CrossRefGoogle Scholar
[W]Welch, P., Some descriptive set theory and core models, Annals of Pure and Applied Logic (to appear).Google Scholar