Recursive functions and metamathematics : problems of completeness and decidability, Gödel's theorems
Author(s)
Bibliographic Information
Recursive functions and metamathematics : problems of completeness and decidability, Gödel's theorems
（Synthese library, v. 286）
Kluwer Academic Publishers, c1999
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Funkcje rekurencyjne i elementy metamatematyki
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Note
Bibliography: p. 341-375
Includes index
Description and Table of Contents
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 Goedel'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.
Table of Contents
Preface. Introduction. 1. Recursive Functions. 2. Goedel's Incompleteness Theorems. 3. Decidability Theory. 4. Philosophical Comments. Bibliography. List of Symbols. Index.
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