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Non-distributive upper semilattice of Kleene degrees

Published online by Cambridge University Press:  12 March 2014

Hisato Muraki
Hisato Muraki*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-Ku, Nagoya 464-8602, Japan, E-mail: [email protected]
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Abstract

K denotes the upper semilattice of all Kleene degrees. Under ZF + AD + DC. K is well-ordered and deg(XSJ) is the next Kleene degree above deg(X) for X ⊆ ωω (see [4] and [5, Chapter V]). While, without AD, properties of K are not always clear. In this note, we prove the non-distributivity of K under ZFC (§1), and that of Kleene degrees between deg(X) and deg(XSJ) for some X under ZFC + CH (§2.3).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 147 - 158
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

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