1st Edition
Inexhaustibility: A Non-Exhaustive Treatment Lecture Notes in Logic 16
By Torkel Franzén
Copyright 2004
263 Pages
by
A K Peters/CRC Press
268 Pages
by
A K Peters/CRC Press
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... Read more
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
Biography
Torkel Franzén Department of Computer Science and Electrical Engineering Lule, University of Technology
"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
