Boolean Valued Analysis

✍ Scribed by A.G. Kusraev, S.S. Kutateladze

• Publisher: Springer
• Year: 1999
• Tongue: English
• Leaves: 335
• Category: Library

✦ Table of Contents

Cover
Title page
Foreword to the English Translation
Preface
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Appendix
References
Subject Index