{"title":"Steven Givant","description":null,"products":[{"product_id":"introduction-to-boolean-algebras-book-steven-givant-9780387402932","title":"Introduction to Boolean Algebras","description":"This book is an informal though systematic series of lectures on Boolean algebras. 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A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised. Most of the corrections were suggested by Peter Crawley. To judge by his detailed and precise suggestions, he must have read every word, checked every reference, and weighed every argument, and I am lIery grateful to hirn for his help. This is not to say that he is to be held responsible for the imperfec­ tions that remain, and, in particular, I alone am responsible for all expressions of personal opinion and irreverent view­ point. P. R. H. Ann Arbor, Michigan ] anuary, 1963 Contents Section Page 1 1 Boolean rings ............................ . 2 Boolean algebras ......................... . 3 9 3 Fields of sets ............................ . 4 Regular open sets . . . . . . . . . . . . . . . . . . . 12 . . . . . . 5 Elementary relations. . . . . . . . . . . . . . . . . . 17 . . . . . 6 Order. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . 7 Infinite operations. . .. . . . . . . . . . . . . . . . . 25 . . . . . 8 Subalgebras . . . . . . . . . . . . . . . . . . . . .. . . . 31 . . . . . . 9 Homomorphisms . . . . . . . . . . . . . . . . . . . . 35 . . . . . . . 10 Free algebras . . . . . . . . . . . . . . . . . . . . . . 40 . . . . . . . 11 Ideals and filters. . . . . . . . . . . . . . . . . . . . 47 . . . . . . 12 The homomorphism theorem. . . . . . . . . . . . .. . . 52 . . 13 Boolean a-algebras . . . . . . . . . . . . . . . . . . 55 . . . . . . 14 The countable chain condition . . . . . . . . . . . . 61 . . . 15 Measure algebras . . . . . . . . . . . . . . . . . . . 64 . . . . . . . 16 Atoms.. . . . .. . . . . .. .. . .. ... . . . . .. . . ... . . .. 69 17 Boolean spaces . . . . . . . . . . . . . . . . . . . . 72 . . . . . . . 18 The representation theorem. . . . . . . . . . . . . . 77 . . . 19 Duali ty for ideals . . . . . . . . . . . . . . . . . .. . . 81 . . . . . 20 Duality for homomorphisms . . . . . . . . . . . . . . 84 . . . . 21 Completion . . . . . . . . . . . . . . . . . . . . . . . 90 . . . . . . . . 22 Boolean a-spaces . . . . . . . . . . . . . . . . . .. . . 97 . . . . . 23 The representation of a-algebras . . . . . . . . .. . . 100 . 24 Boolean measure spaces . . . . . . . . . . . . . .. . . 104 . . . 25 Incomplete algebras . . . . . . . . . . . . . . . .. . . 109 . . . . . 26 Products of algebras . . . . . . . . . . . . . . . .. . . 115 . . . . 27 Sums of algebras . . . . . . . . . . . . . . . . . .. . . 119 . . . . . 28 Isomorphisms of factors . . . . . . . . . . . . . .. . . 122 . . .","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52126254661905,"sku":"NLS9780387900940","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387900940.jpg?v=1757474844"},{"product_id":"introduction-to-boolean-algebras-book-steven-givant-9781441923240","title":"Introduction to Boolean Algebras","description":"This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52332092752145,"sku":"NLS9781441923240","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52749301645585,"sku":"NIN9781441923240","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781441923240.jpg?v=1758150506"},{"product_id":"duality-theories-for-boolean-algebras-with-operators-book-steven-givant-9783319067421","title":"Duality Theories for Boolean Algebras with Operators","description":"In this new text, Steven Givantthe author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarskidevelops three theories of duality for Boolean algebras with operators.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52402601230609,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52402601984273,"sku":"NLS9783319067421","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319067421.jpg?v=1758758275"},{"product_id":"duality-theories-for-boolean-algebras-with-operators-book-steven-givant-9783319350264","title":"Duality Theories for Boolean Algebras with Operators","description":"In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52456149483793,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52456150106385,"sku":"NLS9783319350264","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319350264.jpg?v=1759376453"},{"product_id":"simple-relation-algebras-book-steven-givant-9783319884684","title":"Simple Relation Algebras","description":"This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics.    The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017).","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52500651933969,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":52500652556561,"sku":"NGR9783319884684","price":0.0,"currency_code":"GBP","in_stock":false}]},{"product_id":"introduction-to-relation-algebras-book-steven-givant-9783319879819","title":"Introduction to Relation Algebras","description":"The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field.    The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured paceand outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field.      Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52500710129937,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":52500710719761,"sku":"NGR9783319879819","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319879819.jpg?v=1760138725"},{"product_id":"advanced-topics-in-relation-algebras-book-steven-givant-9783319881362","title":"Advanced Topics in Relation Algebras","description":"The second volume of a pair that charts relation algebras from novice to expert level, this text brings the well-grounded reader to the frontiers of research. Building on the foundations established in the preceding Introduction to Relation Algebras, this volume advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators.  Arranged in a modular fashion, this text offers the opportunity to explore any of several areas in detail; topics include canonical extensions, completions, representations, varieties, and atom structures. Each chapter offers a complete account of one such avenue of development, including a historical section and substantial number of exercises. The clarity of exposition and comprehensive nature of each module make this an ideal text for the independent reader entering the field, while researchers will value it as a reference for years to come.     Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community. Note that this volume contains numerous, essential references to the previous volume, Introduction to Relation Algebras. The reader is strongly encouraged to secure at least electronic access to the first book in order to make use of the second.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52500904313105,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":52500904837393,"sku":"NGR9783319881362","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319881362.jpg?v=1760139186"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-steven-givant.oembed","provider":"World of Books ","version":"1.0","type":"link"}