Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-29T20:05:23.395Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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