Format:
1 Online-Ressource (80 Seiten)
ISBN:
9781108981972
Series Statement:
Cambridge elements
Content:
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.
Note:
Literaturverzeichnis: Seite 71-80
Additional Edition:
ISBN 9781108986991
Additional Edition:
Erscheint auch als Druck-Ausgabe Kennedy, Juliette, 1955 - Gödel's incompleteness theorems Cambridge : Cambridge University Press, 2022 ISBN 9781108986991
Language:
English
Subjects:
Mathematics
,
Philosophy
Keywords:
Gödelscher Unvollständigkeitssatz
DOI:
10.1017/9781108981972
Author information:
Kennedy, Juliette 1955-
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