This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arith...

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Bibliographic Details

Main Author:	Kennedy, Juliette 1955- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cambridge Cambridge University Press 2022
Subjects:	Gödel's theorem Incompleteness theorems Logic, Symbolic and mathematical Gödelscher Unvollständigkeitssatz
Online Access:	BSB01 UBG01 Volltext
Summary:	This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H. Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g. Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued. It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature
Item Description:	Title from publisher's bibliographic system (viewed on 06 Apr 2022)
Physical Description:	1 Online-Ressource (80 Seiten)
ISBN:	9781108981972
DOI:	10.1017/9781108981972