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Branching in the $${\Sigma^0_2}$$ -enumeration degrees: a new perspective

Branching in the $${\Sigma^0_2}$$ -enumeration degrees: a new perspective We give an alternative and more informative proof that every incomplete $${\Sigma^{0}_{2}}$$ -enumeration degree is the meet of two incomparable $${\Sigma^{0}_{2}}$$ -degrees, which allows us to show the stronger result that for every incomplete $${\Sigma^{0}_{2}}$$ -enumeration degree a, there exist enumeration degrees x 1 and x 2 such that a, x 1, x 2 are incomparable, and for all b  ≤  a, b  =  (b ∨ x 1 ) ∧ (b ∨ x 2 ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Branching in the $${\Sigma^0_2}$$ -enumeration degrees: a new perspective

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer-Verlag
Subject
Mathematics; Algebra; Mathematics, general; Mathematical Logic and Foundations
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-008-0081-7
Publisher site
See Article on Publisher Site

Abstract

We give an alternative and more informative proof that every incomplete $${\Sigma^{0}_{2}}$$ -enumeration degree is the meet of two incomparable $${\Sigma^{0}_{2}}$$ -degrees, which allows us to show the stronger result that for every incomplete $${\Sigma^{0}_{2}}$$ -enumeration degree a, there exist enumeration degrees x 1 and x 2 such that a, x 1, x 2 are incomparable, and for all b  ≤  a, b  =  (b ∨ x 1 ) ∧ (b ∨ x 2 ).

Journal

Archive for Mathematical LogicSpringer Journals

Published: Jun 7, 2008

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