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Continuity, proof systems and the theory of transfinite computations
Archive for Mathematical Logic 41 (8):765-788 (2002)
Abstract
We use the theory of domains with totality to construct some logics generalizing ω-logic and β-logic and we prove a completenes theorem for these logics. The key application is E-logic, the logic related to the functional 3E. We prove a compactness theorem for sets of sentences semicomputable in 3E.Author's Profile
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References found in this work
Total sets and objects in domain theory.Ulrich Berger - 1993 - Annals of Pure and Applied Logic 60 (2):91-117.
Domain interpretations of martin-löf’s partial type theory.Erik Palmgren & Viggo Stoltenberg-Hansen - 1990 - Annals of Pure and Applied Logic 48 (2):135-196.
Total objects in inductively defined types.Lill Kristiansen & Dag Normann - 1997 - Archive for Mathematical Logic 36 (6):405-436.
Closing the gap between the continuous functionals and recursion in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $^3E$\end{document}. [REVIEW]Dag Normann - 1997 - Archive for Mathematical Logic 36 (4-5):269-287.
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