Inexhaustibility: A Non-Exhaustive Treatment (Lecture Notes in Logic) - Softcover

Franzén, Torkel

Softcover

ISBN 10: 1568811756 ISBN 13: 9781568811758

Publisher: A K Peters/CRC Press, 2004

Synopsis

Gödel's Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results necessary to understand the arguments are introduced as needed, making the presentation self-contained and thorough.

About this title

Review

 "In this book the author discusses Gödel's famous incompleteness theorems. Special emphasis is put on the consequences of the inexhaustibility of our mathematical knowledge in any one formal axiomatic theory ... The book can be considered as a more technical companion to the author's more philosophical book [Gödel's Theorem, A K Peters, Wellesley, MA, 2005]." -Mathematiacl Reviews, November 2007

Edition details

• Publisher: A K Peters/CRC Press
• Publication date: 2004
• ISBN 10: 1568811756
• ISBN 13: 9781568811758
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 268