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Ultrafilters Throughout Mathematics
About this Title
Isaac Goldbring, University of California, Irvine, Irvine, CA
Publication: Graduate Studies in Mathematics
Publication Year:
2022; Volume 220
ISBNs: 978-1-4704-6900-9 (print); 978-1-4704-6960-3 (online)
DOI: https://doi.org/10.1090/gsm/220
Table of Contents
Download chapters as PDF
Front/Back Matter
Ultrafilters and their applications
- Ultrafilter basics
- Arrow’s theorem on fair voting
- Ultrafilters in topology
- Ramsey theory and combinatorial number theory
- Foundational concerns
Classical ultraproducts
- Classical ultraproducts
- Applicationis to geometry, commutative algebra, and number theory
- Ultraproducts and saturation
- Nonstandard analysis
- Limit groups
Metric ultraproducts and their applications
Advanced topics
Appendices
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