Inexhaustibility: A Non-Exhaustive Treatment: Lecture Notes in Logic 16

ISBN-13: 9781568811741 / Angielski / Twarda / 2004 / 263 str.

Torkel Franzen; Torkel Franza(c)N

Opis

This text is concerned with the concept that our mathematical knowledge is inexhaustible. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems.

Recenzje

 "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

Spis treści

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

O autorze

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