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/lp/springer-journals/where-is-the-g-del-point-hiding-gentzen-s-consistency-proof-of-1936-HuquuwQejq
- Publisher
- Springer International Publishing
- Copyright
- © The Author(s) 2014
- ISBN
- 978-3-319-02170-6
- Pages
- 11 –28
- DOI
- 10.1007/978-3-319-02171-3_2
- Publisher site
- See Chapter on Publisher Site
Abstract
[The calculus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textit{NLK}}$$\end{document} and further notions preliminary to the 1936 consistency proof are defined in this chapter. The most important notion is endform which represents sequents whose validity can be decided. Reduction steps for sequents, whose task is to reduce sequents to endform, are presented. Furthermore, an algorithm for reducing initial sequents to endform is defined and a detailed overview of the consistency proof is given. The chapter ends with a modification of the calculus and the most important rule of the new calculus, chain rule, which can be seen as a generalized cut, is discussed. The modification of the calculus is necessary because it makes the definition of reduction steps for derivations easier.]
Published: Oct 23, 2013
Keywords: Sequent; Calculus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textit{NLK}}$$\end{document}; Natural deduction; Natural deduction in sequent calculus style; Endform; Chain rule; Reduction steps; Reduction steps for sequents