MARC details
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03846cam a2200445 i 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
CUTN |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20231215152834.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
211112s2022 riu b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470469009 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470469610 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9781470469603 |
| 041 ## - LANGUAGE CODE |
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| Language |
English |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
pcc |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
511.3 |
| Edition number |
23/eng/20220112 |
| Item number |
GOL |
| 084 ## - OTHER CLASSIFICATION NUMBER |
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| Classification number |
03C20 |
| -- |
54D80 |
| -- |
03H05 |
| -- |
03E55 |
| -- |
03C50 |
| Source of number |
msc |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Goldbring, Isaac, |
| 245 10 - TITLE STATEMENT |
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| Title |
Ultrafilters throughout mathematics / |
| Statement of responsibility, etc |
Isaac Goldbring. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xviii, 399 pages ; |
| Dimensions |
26 cm. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
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| Volume number/sequential designation |
v.220 |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
Ultrafilters and their applications<br/>Ultrafilter basics<br/>Arrow’s theorem on fair voting<br/>Ultrafilters in topology<br/>Ramsey theory and combinatorial number theory<br/>Foundational concerns<br/>Classical ultraproducts<br/>Classical ultraproducts<br/>Applicationis to geometry, commutative algebra, and number theory<br/>Ultraproducts and saturation<br/>Nonstandard analysis<br/>Limit groups<br/>Metric ultraproducts and their applications<br/>Metric ultraproducts<br/>Asymptotic cones and Gromov’s theorem<br/>Sofic groups<br/>Functional analysis<br/>Advanced topics<br/>Does an ultrapower depend on the ultrafilter?<br/>The Keisler-Shelah theorem<br/>Large cardinals<br/>Appendices<br/>Logic<br/>Set theory<br/>Category theory<br/>Hints and solutions to selected exercises |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Graduate Studies in Mathematics<br/>Volume: 220; 2022; 399 pp<br/>MSC: Primary 03; 54;<br/>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.<br/><br/>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 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Ultrafilters (Mathematics) |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical logic and foundations -- Model theory -- Ultraproducts and related constructions. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
General topology -- Fairly general properties of topological spaces -- Special constructions of topological spaces (spaces of ultrafilters, etc.). |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical logic and foundations -- Nonstandard models -- Nonstandard models in mathematics. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical logic and foundations -- Set theory -- Large cardinals. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical logic and foundations -- Model theory -- Models with special properties (saturated, rigid, etc.). |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Department Name |
Mathematics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Project book |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Relator term |
author. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Graduate studies in mathematics, |
| International Standard Serial Number |
1065-7339 ; |
| Volume number/sequential designation |
220 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references (pages 385-394) and index. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Source of heading or term |
msc |
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4 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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msc |
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4 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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msc |
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4 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Source of heading or term |
msc |
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4 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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msc |
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4 |
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7 |
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cbc |
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orignew |
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