Induction and Sets

The book is an introduction to mathematical logic and set theory. It contains everything that is expected from such a book - language, syntax, semantics, model, deducibility, completeness theorem, normal form theorem, recursion and axioms of ZFC. The style of the book differs from similar textbooks. The central notion in the book is a recursive data type, which means a set defined by a recursion. This notion is introduced early, hence some knowledge of set theory is tacitly assumed at the very beginning (and it also induces some circular arguments at the end). The whole presentation is not as rigorous as could be expected in textbooks of this type. On the other hand, the book contains a lot of philosophical explanations pointing to aspects usually ignored. Another interesting point is that the set of exercises contains some, which are rare to meet, for example: “Dress up the traditional proof that Ö2 is irrational into a proof by well-founded induction on N x N.” Once you are familiar with a classical textbook on the topics, reading this one as a second choice is fun.

Reviewer: 
psi
Book details
Author:  Publisher: 
Published: 
2003
ISBN: 
0-521-53361-9, ISBN 0-521-82621-7
Price: 
£18,95
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