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Some new natural α-re-degrees

Published online by Cambridge University Press:  12 March 2014

Colin G. Bailey
Colin G. Bailey*
Affiliation:
Department of Mathematics, Victoria University, Wellington, New Zealand
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Abstract

If α is a singular cardinal (either real or fake) in L, I exhibit many natural α-re subsets, defined uniformly from the ⊿1 subsets of a. If α. is a true cardinal this provides an uppersemilattice (usl) embedding from the lattice of ⊿1 subsets of α into the usl of α-re-degrees. It will also be shown that this embedding cannot be extended to the Σ 1 subsets of α.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 1 , March 1987 , pp. 227 - 231
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCES

[1] Chong, C. T. and Friedman, S. D., Degree theory on ℵ ω , Annals of Pure and Applied Logic, vol. 24 (1983), pp. 87–97.CrossRefGoogle Scholar
[2] Friedman, S. D., Natural α-re degrees, Logic year 1979–1980 (Lerman, M. et al., editors), Lecture Notes in Mathematics, vol. 859, Springer-Verlag, Berlin, 1981, pp. 63–66.CrossRefGoogle Scholar
[3] Lachlan, A. H., Lower bounds for pairs of r.e. degrees, Proceedings of the London Mathematical Society, ser. 3, vol. 10 (1966), pp. 537–566.CrossRefGoogle Scholar