Recursive Functions and Metamathematics

Problems of Completeness and Decidability, Gödel's Theorems
1999
ISBN: 978-0-7923-5904-3
Verlag: Springer Netherlands

Buch, Englisch, 395 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1630 g

Reihe: Synthese Library

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.
Scholars and advanced students of logic, mathematics, philosophy of science.

Zielgruppe

Research

Autoren/Hrsg.

Murawski, Roman

Fachgebiete

• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

1 Recursive Functions.- 2 Gödel’s Incompleteness Theorems.- 3 Decidability Theory.- 4 Philosophical Comments.- List of Symbols.