## Works by Matthew B. Giorgi

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1. The computably enumerable degrees are locally non-cappable.Matthew B. Giorgi - 2004 - Archive for Mathematical Logic 43 (1):121-139.
We prove that every non-computable incomplete computably enumerable degree is locally non-cappable, and use this result to show that there is no maximal non-bounding computably enumerable degree.

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2. The computably enumerable degrees are locally non-cappable.Matthew B. Giorgi - 2003 - Archive for Mathematical Logic -1 (1):1-1.

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3. A high c.e. degree which is not the join of two minimal degrees.Matthew B. Giorgi - 2010 - Journal of Symbolic Logic 75 (4):1339-1358.
We construct a high c.e. degree which is not the join of two minimal degrees and so refute Posner's conjecture that every high c.e. degree is the join of two minimal degrees. Additionally, the proof shows that there is a high c.e. degree a such that for any splitting of a into degrees b and c one of these degrees bounds a 1-generic degree.

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4. A high noncuppable $${\Sigma^0_2}$$ e-degree.Matthew B. Giorgi - 2008 - Archive for Mathematical Logic 47 (3):181-191.
We construct a ${\Sigma^0_2}$ e-degree which is both high and noncuppable. Thus demonstrating the existence of a high e-degree whose predecessors are all properly ${\Sigma^0_2}$.
5. We construct a \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}e-degree which is both high and noncuppable. Thus demonstrating the existence of a high e-degree whose predecessors are all properly \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}.