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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.
Ernest Schimmerling is a Professor of Mathematical Sciences at Carnegie Mellon University.
Note to the instructor; Acknowledgments; 1. Preliminaries; 2. ZFC; 3. Order; 4. Cardinality; 5. Trees; 6. Dense linear orderings; 7. Filters and ideals; Appendix. Summary of exercises on Boolean algebra; Index.
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- ID: 9781107400481
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