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Low5 Boolean Subalgebras and Computable Copies

Published online by Cambridge University Press:  12 March 2014

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: Russell.Miller@qc.cuny.edu, URL: www.qc.edu/~rmiller

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
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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