Inexhaustibility: A Non-Exhaustive Treatment

Lecture Notes in Logic 16
 
 
A K Peters (Verlag)
  • 1. Auflage
  • |
  • erschienen am 2. September 2004
 
  • Buch
  • |
  • Hardcover
  • |
  • 263 Seiten
978-1-56881-174-1 (ISBN)
 
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.
  • Englisch
  • Natick
  • |
  • USA
Taylor & Francis Inc
  • Für höhere Schule und Studium
  • |
  • Für Beruf und Forschung
  • Höhe: 229 mm
  • |
  • Breite: 152 mm
  • 499 gr
978-1-56881-174-1 (9781568811741)
1568811748 (1568811748)
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"In this book the author discusses Goedel'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 [Goedel's Theorem, A K Peters, Wellesley, MA, 2005]." -Mathematiacl Reviews, November 2007

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