Notes on Set Theory

Front Cover
Springer Science & Business Media, 1994 - Axiomatische Mengenlehre - 272 pages
0 Reviews
"The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets (including the basic results that have applications to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets." "Topics covered include the naive theory of equinumerosity; paradoxes and axioms; modeling mathematical notions by sets; cardinal numbers; natural numbers; fixed points (continuous least-fixed-point theorem); well-ordered sets (transfinite induction and recursion, Hartogs' theorem, comparability of well-ordered sets, least-fixed-point theorem); the Axiom of Choice and its consequences; Baire space (Cantor-Bendixson theorem, analytic pointsets, perfect set theorem); Replacement and other axioms; ordinal numbers. There is an Appendix on the real numbers and another on natural models, including the antifounded universe." "The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy."--Jacket.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Problems for Chapter 1
1
Paradoxes and axioms
19
Are sets all there is?
33
The natural numbers
53
Fixed points
73
Well ordered sets
93
Choices
117
Baire space
147
Replacement and other axioms
169
Ordinal numbers
189
A The real numbers
209
B Axioms and universes
239
Index
267
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information