Book:Alan G. Hamilton/Numbers, Sets and Axioms
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Alan G. Hamilton: Numbers, Sets and Axioms: The Apparatus of Mathematics
Published $\text {1982}$, Cambridge University Press
- ISBN 0-521-28761-8
Subject Matter
Contents
- Preface
- 1 Numbers
- 1.1 Natural numbers and integers
- 1.2 Rational numbers
- 1.3 Real numbers
- 1.4 Decimal notation
- 2 The size of a set
- 2.1 Finite and countable sets
- 2.2 Uncountable sets
- 2.3 Cardinal numbers
- 3 Ordered sets
- 3.1 Order relations and ordered sets
- 3.2 Lattices and Boolean algebras
- 4 Set theory
- 4.1 What is a set?
- 4.2 The Zermelo-Fraenkel axioms
- 4.3 Mathematics in ZF
- 4.4 Sets and classes
- 4.5 Models of set theory
- 5 The axiom of choice
- 5.1 The axiom of choice and direct applications
- 5.2 Zorn's lemma and the well-ordering theorem
- 5.3 Other consequences of the axiom of choice
- 6 Ordinal and cardinal numbers
- 6.1 Well-ordered sets and ordinal numbers
- 6.2 Transfinite recursion and ordinal arithmetic
- 6.3 Cardinal numbers
- Hints and solutions to selected exercises
- References
- Index of symbols
- Subject index
Source work progress
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