Goedel's Incompleteness Theorems (Paperback, New Ed)

This Element takes a deep dive into Goedel'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 Goedel'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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Elements in Philosophy and Logic
Release date:	April 2022
Authors:	Juliette Kennedy
Dimensions:	229 x 152 x 5mm (L x W x T)
Format:	Paperback - Trade
Pages:	75
Edition:	New Ed
ISBN-13:	978-1-108-98699-1
Categories:	Books > Humanities > Philosophy > Topics in philosophy > Logic Books > Science & Mathematics > Mathematics > Mathematical foundations > Set theory Books > Philosophy > Topics in philosophy > Logic
LSN:	1-108-98699-4
Barcode:	9781108986991

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