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

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

by Torkel Franzen
     
 

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ISBN-10: 1568811756

ISBN-13: 9781568811758

Pub. Date: 09/02/2004

Publisher: Taylor & Francis

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

Overview

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:
9781568811758
Publisher:
Taylor & Francis
Publication date:
09/02/2004
Series:
Lecture Notes in Logic Series
Pages:
263
Product dimensions:
6.00(w) x 8.90(h) x 0.60(d)

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