Ultrafilters Throughout Mathematics

ISBN-13: 9781470469610 / Miękka / 2022

Isaac Goldbring

Spis treści

• 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: Metric ultraproducts
• Asymptotic cones and Gromov's theorem
• Sofic groups
• Functional analysis
• Advanced topics: Does an ultrapower depend on the ultrafilter?
• The Keisler-Shelah theorem
• Large cardinals
• Appendices: Logic
• Set theory
• Category theory
• Hints and solutions to selected exercises
• Bibliography
• Index