Boolean Algebras

Boolean Algebras by Roman Sikorski.

There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due t...

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Bibliographic Details
Main Author: Sikorski, Roman (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1969.
Edition:3rd ed. 1969.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics ; 25
Springer eBook Collection.
Subjects:
Mathematical logic.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I. Finite joins and meets
  • § 1. Definition of Boolean algebras
  • § 2. Some consequences of the axioms
  • § 3. Ideals and filters
  • § 4. Subalgebras
  • § 5. Homomorphisms, isomorphisms
  • § 6. Maximal ideals and filters
  • § 7. Reduced and perfect fields of sets
  • § 8. A fundamental representation theorem
  • § 9. Atoms
  • § 10. Quotient algebras
  • §11. Induced homomorphisms between fields of sets
  • § 12. Theorems on extending to homomorphisms
  • § 13. Independent subalgebras. Products
  • § 14. Free Boolean algebras
  • § 15. Induced homomorphisms between quotient algebras
  • § 16. Direct unions
  • § 17. Connection with algebraic rings
  • II. Infinite joins and meets
  • § 18. Definition
  • § 19. Algebraic properties of infinite joins and meets. (m, n)-distributivity.
  • § 20. m-complete Boolean algebras
  • § 21. m-ideals and m-filters. Quotient algebras
  • § 22. m-homomorphisms. The interpretation in Stone spaces
  • § 23. m-subalgebras
  • § 24. Representations by m-fields of sets
  • § 25. Complete Boolean algebras
  • § 26. The field of all subsets of a set
  • §27. The field of all Borel subsets of a metric space
  • §28. Representation of quotient algebras as fields of sets
  • § 29. A fundamental representation theorem for Boolean ?-algebras. m-representability
  • § 30. Weak m-distributivity
  • § 31. Free Boolean m-algebras
  • § 32. Homomorphisms induced by point mappings
  • § 33. Theorems on extension of homomorphisms
  • § 34. Theorems on extending to homomorphisms
  • § 35. Completions and m-completions
  • § 36. Extensions of Boolean algebras
  • § 37. m-independent subalgebras. The field m-product
  • § 38. Boolean (m, n)-products
  • § 39. Relation to other algebras
  • § 40. Applications to mathematical logic. Classical calculi
  • § 41. Topology in Boolean algebras. Applications to non-classical logic
  • § 42. Applications to measure theory
  • § 43. Measurable functions and real homomorphisms
  • § 44. Measurable functions. Reduction to continuous functions
  • § 45. Applications to functional analysis
  • § 46. Applications to foundations of the theory of probability
  • § 47. Problems of effectivity
  • List of symbols
  • Author Index.

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