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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\omega $$\end{document}-enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\omega $$\end{document}-enumeration degrees.
Archive for Mathematical Logic – Springer Journals
Published: Nov 1, 2021
Keywords: Degree structures; Enumeration reducibility; Jump; Definability; 03D28; 03D30
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