ISBN 9788132206675,Notes on Set Theory

Notes on Set Theory

Publisher:

Springer

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ISBN 9788132206675
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ISBN 9788132206675
Publisher

Springer

Publication Year 2012
ISBN-13

ISBN 9788132206675

ISBN-10 8132206673
Binding

Paperback

Edition 2nd
Number of Pages 284 Pages
Language (English)
Subject

Educational: Mathematics & numeracy

ndation 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, but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author added solutions to the exercises, and rearranged and reworked the text in several places to improve the presentation. The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy.

Table of Contents

Introduction
Equinumerosity
Paradoxes and axioms
Are sets all there is?
The natural numbers
Fixed points
Well ordered sets
Choices
Choice's consequences
Baire space
Replacement and other axioms
Ordinal numbers
A. The real numbers
B. Axioms and universes
Index.

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