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Introduction to Boolean Algebras

  • Authors
  • Paul  Halmos
  • Steven Givant

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages 1-14
  2. Steven Givant
    Pages 1-7
  3. Steven Givant
    Pages 8-13
  4. Steven Givant
    Pages 14-19
  5. Steven Givant
    Pages 20-23
  6. Steven Givant
    Pages 24-30
  7. Steven Givant
    Pages 31-37
  8. Steven Givant
    Pages 38-44
  9. Steven Givant
    Pages 45-52
  10. Steven Givant
    Pages 53-65
  11. Steven Givant
    Pages 66-73
  12. Steven Givant
    Pages 74-88
  13. Steven Givant
    Pages 89-104
  14. Steven Givant
    Pages 105-116
  15. Steven Givant
    Pages 117-126
  16. Steven Givant
    Pages 127-133
  17. Steven Givant
    Pages 134-141
  18. Steven Givant
    Pages 142-148
  19. Steven Givant
    Pages 149-163
  20. Steven Givant
    Pages 164-170
  21. Steven Givant
    Pages 171-177
  22. Steven Givant
    Pages 178-187
  23. Steven Givant
    Pages 188-192
  24. Steven Givant
    Pages 193-199
  25. Steven Givant
    Pages 200-213
  26. Steven Givant
    Pages 214-220
  27. Steven Givant
    Pages 221-242
  28. Steven Givant
    Pages 243-255
  29. Steven Givant
    Pages 256-267
  30. Steven Givant
    Pages 268-281
  31. Steven Givant
    Pages 282-287
  32. Steven Givant
    Pages 288-299
  33. Steven Givant
    Pages 300-311
  34. Steven Givant
    Pages 312-325
  35. Steven Givant
    Pages 326-337
  36. Steven Givant
    Pages 338-346
  37. Steven Givant
    Pages 347-358
  38. Steven Givant
    Pages 359-367
  39. Steven Givant
    Pages 368-372
  40. Steven Givant
    Pages 373-377
  41. Steven Givant
    Pages 378-383
  42. Steven Givant
    Pages 384-389
  43. Steven Givant
    Pages 390-395
  44. Steven Givant
    Pages 396-421
  45. Steven Givant
    Pages 422-438
  46. Steven Givant
    Pages 439-446
  47. Back Matter
    Pages 1-128

About this book

Introduction

In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of college-level mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebra --- and in particular to the important interconnections with topology --- without assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself.

 

Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski’s isomorphism of factors theorem for countably complete Boolean algebras, and Hanf’s related counterexamples; and an extensive treatment of the algebraic-topological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and Stone-Cech compactifications.

 

A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course.

Keywords

Boolean algebra Division Lattice algebra homomorphism set theory

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-68436-9
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-40293-2
  • Online ISBN 978-0-387-68436-9
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site
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