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Every 1-generic computes a properly 1-generic

Published online by Cambridge University Press:  12 March 2014

Barbara F. Csima ,
Rod Downey ,
Noam Greenberg ,
Denis R. Hirschfeldt  and
Joseph S. Miller
Barbara F. Csima
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON. N2L 3G1., Canada, E-mail: [email protected]
Rod Downey
Affiliation:
School of Mathematics, Statistics and Computer Science, Victoria University, P.O. Box 600 Wellington. New Zealand, E-mail: [email protected]
Noam Greenberg
Affiliation:
School of Mathematics, Statistics and Computer Science, Victoria University, P.O. Box 600 Wellington. New Zealand, E-mail: [email protected]
Denis R. Hirschfeldt
Affiliation:
Mathematics Department, University of Chicago, 5734 S. University Ave. Chicago. IL 60637., USA, E-mail: [email protected]
Joseph S. Miller
Affiliation:
Mathematics Department, University of Connecticut, Storrs, CT 06269., USA, E-mail: [email protected]
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Abstract

A real is called properly n-generic if it is n-generic but not n + 1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1385 - 1393
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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