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Generalized high degrees have the complementation property

Published online by Cambridge University Press:  12 March 2014

Noam Greenberg,
Antonio Montalbán and
Richard A. Shore
Noam Greenberg
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853, USA, E-mail: erlkonig@math.cornell.edu
Antonio Montalbán
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853, USA, E-mail: antonio@math.cornell.edu
Richard A. Shore
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853, USA, E-mail: shore@math.cornell.edu
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Abstract.

We show that if d ∈ GH1 then (≤ d) has the complementation property, i.e., for all a < d there is some b < d such that a ∧ b = 0 and a ∨ b = d.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 4 , December 2004, pp. 1200 - 1220
Copyright
Copyright © Association for Symbolic Logic 2004

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