ENGLISH

Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel’s Theorems

By Roman Murawski (auth.)

Book information

Publisher
Springer Netherlands
Year
1999
ISBN
978-90-481-5298-8, 978-94-017-2866-9
DOI
10.1007/978-94-017-2866-9
Language
english
Format
PDF
Filesize
13 MB (13526840 bytes)
Series
Synthese Library 286
Edition
1
Pages
395\402
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Logic; Mathematical Logic and Foundations; Philoso

Description

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

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