Boolean Valued Analysis

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.