Boolean Algebras
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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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1969, 1969
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| Edition: | 3rd ed. 1969 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- § 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
- 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