A Course on Set Theory

Ernest Schimmerling

doi:10.1017/CBO9780511996351

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretical fundamentals, the author proceeds to illustrate applications to topology, analysis and combinatorics, as well as to pure set theory. Concepts such as Boolean algebras, trees, games, dense linear orderings, ideals, filters and club and stationary sets are also developed. Pitched specifically at undergraduate students, the approach is neither esoteric nor encyclopedic. The author, an experienced instructor, includes motivating examples and over 100 exercises designed for homework assignments, reviews and exams. It is appropriate for undergraduates as a course textbook or for self-study. Graduate students and researchers will also find it useful as a refresher or to solidify their understanding of basic set theory.

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A Course on Set Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Note to the instructor
pp vii-ix

Acknowledgements
pp x-x

1 - Preliminaries
pp 1-6

2 - ZFC
pp 7-21

3 - Order
pp 22-52

4 - Cardinality
pp 53-81

5 - Trees
pp 82-124

6 - Dense linear orderings
pp 125-140

7 - Filters and ideals
pp 141-162

Appendix Summary of exercises on Boolean algebra
pp 163-163

Selected further reading
pp 164-165

Bibliography
pp 166-166

Index
pp 167-168

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A Course on Set Theory

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