Inexhaustibility

A Non-Exhaustive Treatment (Lecture Notes in Logic #16)

Torkel Franzén

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English

A K Peters
02 September 2004

Mathematical logic

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.

By: Torkel Franzén
Imprint: A K Peters
Country of Publication: United States
Volume: No. 16
Dimensions: Height: 229mm, Width: 152mm, Spine: 14mm
Weight: 362g
ISBN: 9781568811758
ISBN 10: 1568811756
Pages: 263
Publication Date: 02 September 2004
Audience: General/trade , College/higher education , Professional and scholarly , ELT Advanced , A / AS level
Format: Paperback
Publisher's Status: Active

CHAPTER l. INTRODUCTION . CHAPTER 2. ARITHMETICAL PRELIMINARIES CHAPTER 3. PRIMES AND PROOFS . CHAPTER 4. THE LANGUAGE OF ARITHMETIC CHAPTER 5. THE LANGUAGE OF ANALYSIS CHAPTER 6. ORDINALS AND INDUCTIVE DEFINITIONS. CHAPTER 7. FORMAL LANGUAGES AND THE DEFINITION OF TRUTH CHAPTER 8. LOGICC AND THEORIES. CHAPTER 9. PEA.NO ARTHMETIC AND COMPUTABILl1Y CHAPTER 9. PEA.NO ARTHMETIC AND COMPUTABILl1Y CHAPTER 10. ELEMENTARY AND CLASSICAL ANALYSIS CHAPTER 11. THE RECURSION THEOREM AND ORDINAL NOTATIONS CHAPTER 12. THE INCOMPLETENESS THEOREMS CHAPTER 13. ITERATED CONSISTENCY CHAPTER 14. ITERATED REFLECTION CHAPTER 15. ITERATED ITERATION AND INEXHAUSTIBILITY

Torkel Franzén Department of Computer Science and Electrical Engineering Lule, University of Technology

Reviews for Inexhaustibility: A Non-Exhaustive Treatment (Lecture Notes in Logic #16)

In this book the author discusses Godel'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 [Godel's Theorem, A K Peters, Wellesley, MA, 2005]. -Mathematiacl Reviews, November 2007