Set Theory and Its Philosophy: A Critical Introduction

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Overview

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

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Product Details

  • ISBN-13: 9780199270415
  • Publisher: Oxford University Press, USA
  • Publication date: 4/15/2004
  • Edition description: New Edition
  • Pages: 360
  • Product dimensions: 9.20 (w) x 6.10 (h) x 0.80 (d)

Meet the Author

Michael Potter is University Lecturer in Philosophy, and Fellow of Fitzwilliam College, at Cambridge. He is the author of Sets (1990), on which the present work draws but which was written for a more specialist readership, and Reason's Nearest Kin (2000).

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Table of Contents

I Sets 1
1 Logic 6
2 Collections 21
3 The hierarchy 34
4 The theory of sets 55
II Numbers 79
5 Arithmetic 88
6 Counting 103
7 Lines 117
8 Real numbers 129
III Cardinals and Ordinals 151
9 Cardinals 155
10 Basic cardinal arithmetic 167
11 Ordinals 175
12 Ordinal arithmetic 191
IV Further Axioms 207
13 Orders of infinity 211
14 The axiom of choice 238
15 Further cardinal arithmetic 261
App. A Traditional axiomatizations 291
App. B Classes 299
App. C Sets and classes 312
References 317
List of symbols 329
Index of definitions 331
Index of names 336
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