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

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

by Torkel Franzen
ISBN-10:
1568811748
ISBN-13:
9781568811741
Pub. Date:
09/02/2004
Publisher:
Taylor & Francis
Select a Purchase Option
  • purchase options

Temporarily Out of Stock Online


Overview

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

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.

Product Details

ISBN-13: 9781568811741
Publisher: Taylor & Francis
Publication date: 09/02/2004
Series: Lecture Notes in Logic Series
Pages: 263
Product dimensions: 6.20(w) x 9.10(h) x 0.80(d)

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews