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Boolean Valued Analysis

Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a charact...

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Bibliographic Details
Main Authors: Kusraev, A.G., Kutateladze, Semën Samsonovich (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1999, 1999
Edition:1st ed. 1999
Series:Mathematics and Its Applications
Subjects:
Difference Equations
Functional Equations
Difference And Functional Equations
Operator Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. Universes of Sets
  • § 1.1. Boolean Algebras
  • § 1.2. Representation of a Boolean Algebra
  • § 1.3. Von Neumann—Gödel—Bernays Theory
  • § 1.4. Ordinals
  • § 1.5. Hierarchies of Sets
  • 2. Boolean Valued Universes
  • § 2.1. The Universe over a Boolean Algebra
  • § 2.2. Transformations of a Boolean Valued Universe
  • § 2.3. Mixing and the Maximum Principle
  • § 2.4. The Transfer Principle
  • § 2.5. Separated Boolean Valued Universes
  • 3. Functors of Boolean Valued Analysis
  • § 3.1. The Canonical Embedding
  • § 3.2. The Descent Functor
  • § 3.3. The Ascent Functor
  • § 3.4. The Immersion Functor
  • § 3.5. Interplay Between the Main Functors
  • 4. Boolean Valued Analysis of Algebraic Systems
  • § 4.1. Algebraic B-Systems
  • § 4.2. The Descent of an Algebraic System
  • § 4.3. Immersion of Algebraic B-Systems
  • § 4.4. Ordered Algebraic Systems
  • § 4.5. The Descent of a Field
  • 5. Boolean Valued Analysis of Banach Spaces
  • § 5.1. Vector Lattices
  • § 5.2. Representation of Vector Lattices
  • § 5.3. Lattice Normed Spaces
  • § 5.4. The Descent of a Banach Space
  • § 5.5. Spaces with Mixed Norm
  • 6. Boolean Valued Analysis of Banach Algebras
  • § 6.1. The Descent of a Banach Algebra
  • § 6.2. AW*-Algebras and AW*-Modules
  • § 6.3. The Boolean Dimension of an AW*-Module
  • § 6.4. Representation of an AW*-Module
  • § 6.5. Representation of a Type I AW*-Algebra
  • § 6.6. Embeddable C*-Algebras
  • References

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