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Low5 Boolean Subalgebras and Computable Copies

Published online by Cambridge University Press:  12 March 2014

Russell Miller
Russell Miller*
Affiliation:
Department of Mathematics, Queens College–C.U.N.Y., 65-30 Kissena Blvd., Flushing, New York 11367, USA PH.D. Programs in Mathematics and Computer Science, C.U.N.Y. Graduate Center, 365 Fifth Avenue, New York, New York 10016, USA, E-mail: [email protected], URL: www.qc.edu/~rmiller
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Abstract

It is known that the spectrum of a Boolean algebra cannot contain a low4 degree unless it also contains the degree 0; it remains open whether the same holds for low5 degrees. We address the question differently, by considering Boolean subalgebras of the computable atomless Boolean algebra . For such subalgebras , we show that it is possible for the spectrum of the unary relation on to contain a low5 degree without containing 0.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 1061 - 1074
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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