Branching in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} -enumeration degrees: a new perspective [Book Review]

Archive for Mathematical Logic 47 (3):221-231 (2008)
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Abstract

We give an alternative and more informative proof that every incomplete \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{2}}$$\end{document} -enumeration degree is the meet of two incomparable \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{2}}$$\end{document} -degrees, which allows us to show the stronger result that for every incomplete \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{2}}$$\end{document} -enumeration degree a, there exist enumeration degrees x1 and x2 such that a, x1, x2 are incomparable, and for all b ≤ a, b = (b ∨ x1 ) ∧ (b ∨ x2 ).

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The density of the nonbranching degrees.Peter A. Fejer - 1983 - Annals of Pure and Applied Logic 24 (2):113-130.
Some Special Pairs of Σ2 e-Degrees.Seema Ahmad & Alistair H. Lachlan - 1998 - Mathematical Logic Quarterly 44 (4):431-449.
Embedding the diamond in the σ2 enumeration degree.Seema Ahmad - 1991 - Journal of Symbolic Logic 56 (1):195 - 212.

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