000			03846cam a2200445 i 4500
003			CUTN
005			20231215152834.0
008			211112s2022 riu b 001 0 eng
020			_a9781470469009
020			_a9781470469610
020			_z9781470469603
041			_aEnglish
042			_apcc
082	0	0	_a511.3 _223/eng/20220112 _bGOL
084			_a03C20 _a54D80 _a03H05 _a03E55 _a03C50 _2msc
100	1		_aGoldbring, Isaac,
100	1		_eauthor.
245	1	0	_aUltrafilters throughout mathematics / _cIsaac Goldbring.
300			_axviii, 399 pages ; _c26 cm.
440			_vv.220
490	0		_aGraduate studies in mathematics, _x1065-7339 ; _v220
504			_aIncludes bibliographical references (pages 385-394) and index.
505			_tUltrafilters 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
520			_aGraduate Studies in Mathematics Volume: 220; 2022; 399 pp MSC: Primary 03; 54; Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes which have applications to many areas of mathematics. Typically, this topic is presented to students in specialized courses such as logic, functional analysis, or geometric group theory. In this book, the basic facts about ultrafilters and ultraproducts are presented to readers with no prior knowledge of the subject and then these techniques are applied to a wide variety of topics. The first part of the book deals solely with ultrafilters and presents applications to voting theory, combinatorics, and topology, while also dealing also with foundational issues. The second part presents the classical ultraproduct construction and provides applications to algebra, number theory, and nonstandard analysis. The third part discusses a metric generalization of the ultraproduct construction and gives example applications to geometric group theory and functional analysis. The final section returns to more advanced topics of a more foundational nature. The book should be of interest to undergraduates, graduate students, and researchers from all areas of mathematics interested in learning how ultrafilters and ultraproducts can be applied to their specialty.
650		0	_aUltrafilters (Mathematics)
650		7	_aMathematical logic and foundations -- Model theory -- Ultraproducts and related constructions.
650		7	_aGeneral topology -- Fairly general properties of topological spaces -- Special constructions of topological spaces (spaces of ultrafilters, etc.).
650		7	_aMathematical logic and foundations -- Nonstandard models -- Nonstandard models in mathematics.
650		7	_aMathematical logic and foundations -- Set theory -- Large cardinals.
650		7	_aMathematical logic and foundations -- Model theory -- Models with special properties (saturated, rigid, etc.).
650		7	_2msc _94
650		7	_2msc _94
650		7	_2msc _94
650		7	_2msc _94
650		7	_2msc _94
690			_aMathematics
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cPROJECT
999			_c40978 _d40978