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Table of Contents
Cover
Title page
Chapter 1. Introduction
1.1. What we knew
1.2. What we wanted
1.3. What we did
1.4. How we proved it
1.5. Classification of non-separable structures up to bi-embeddability
1.6. Organization of the paper, or: How (not) to read this paper
1.7. Annotated content
Chapter 2. Preliminaries and notation
2.1. Basic notions
2.2. Choice and determinacy
2.3. Cardinality
2.4. Algebras of sets
2.5. Descriptive set theory
2.6. Trees and reductions
Chapter 3. The generalized Cantor space
3.1. Basic facts
3.2. *More on 2^{ }
Chapter 4. Generalized Borel sets
4.1. Basic facts
4.2. Intermezzo: the projective ordinals
4.3. *More on generalized Borel sets
Chapter 5. Generalized Borel functions
5.1. Basic facts
5.2. *Further results
Chapter 6. The generalized Baire space and Baire category
6.1. The generalized Baire space
6.2. Baire category
Chapter 7. Standard Borel -spaces, -analytic quasi-orders, and spaces of codes
7.1. -analytic sets
7.2. Spaces of type and spaces of codes
Chapter 8. Infinitary logics and models
8.1. Infinitary logics
8.2. Some generalizations of the Lopez-Escobar theorem
Chapter 9. -Souslin sets
9.1. Basic facts
9.2. More on Souslin sets and Souslin cardinals
9.3. Souslin sets and cardinals in models with choice
9.4. Souslin sets and cardinals in models of determinacy
Chapter 10. The main construction
10.1. The combinatorial trees ₀ and ₁
10.2. The combinatorial trees _{ }
Chapter 11. Completeness
11.1. Faithful representations of -Souslin quasi-orders
11.2. The quasi-order ≤_{max} and the reduction Σ_{ }
11.3. Reducing ≤_{max}^{ } to \embeds^{ }_{\CT}
11.4. Some absoluteness results
Chapter 12. Invariant universality.
12.1. An \LL_{ ⁺ }-sentence \Uppsi describing the structures _{ }.
12.2. A classification of the structures in \Mod^{ }_{\Uppsi} up to isomorphism
12.3. The invariant universality of \embeds^{ }_{\CT}
12.4. More absoluteness results
Chapter 13. An alternative approach
13.1. Completeness
13.2. Invariant universality
Chapter 14. Definable cardinality and reducibility
14.1. Topological complexity
14.2. Absolutely definable reducibilities
14.3. Reducibilities in an inner model
Chapter 15. Some applications
15.1. \bSigma¹₂ quasi-orders
15.2. Projective quasi-orders
15.3. More complex quasi-orders in models of determinacy
15.4. \Ll(\R)-reducibility
Chapter 16. Further completeness results
16.1. Representing arbitrary partial orders as embeddability relations
16.2. Other model theoretic examples
16.3. Isometry and isometric embeddability between complete metric spaces of density character
16.4. Linear isometry and linear isometric embeddability between Banach spaces of density
16.5. *Further results on the classification of nonseparable metric and Banach spaces
Indexes
Index
Index
Bibliography
Back Cover.
Title page
Chapter 1. Introduction
1.1. What we knew
1.2. What we wanted
1.3. What we did
1.4. How we proved it
1.5. Classification of non-separable structures up to bi-embeddability
1.6. Organization of the paper, or: How (not) to read this paper
1.7. Annotated content
Chapter 2. Preliminaries and notation
2.1. Basic notions
2.2. Choice and determinacy
2.3. Cardinality
2.4. Algebras of sets
2.5. Descriptive set theory
2.6. Trees and reductions
Chapter 3. The generalized Cantor space
3.1. Basic facts
3.2. *More on 2^{ }
Chapter 4. Generalized Borel sets
4.1. Basic facts
4.2. Intermezzo: the projective ordinals
4.3. *More on generalized Borel sets
Chapter 5. Generalized Borel functions
5.1. Basic facts
5.2. *Further results
Chapter 6. The generalized Baire space and Baire category
6.1. The generalized Baire space
6.2. Baire category
Chapter 7. Standard Borel -spaces, -analytic quasi-orders, and spaces of codes
7.1. -analytic sets
7.2. Spaces of type and spaces of codes
Chapter 8. Infinitary logics and models
8.1. Infinitary logics
8.2. Some generalizations of the Lopez-Escobar theorem
Chapter 9. -Souslin sets
9.1. Basic facts
9.2. More on Souslin sets and Souslin cardinals
9.3. Souslin sets and cardinals in models with choice
9.4. Souslin sets and cardinals in models of determinacy
Chapter 10. The main construction
10.1. The combinatorial trees ₀ and ₁
10.2. The combinatorial trees _{ }
Chapter 11. Completeness
11.1. Faithful representations of -Souslin quasi-orders
11.2. The quasi-order ≤_{max} and the reduction Σ_{ }
11.3. Reducing ≤_{max}^{ } to \embeds^{ }_{\CT}
11.4. Some absoluteness results
Chapter 12. Invariant universality.
12.1. An \LL_{ ⁺ }-sentence \Uppsi describing the structures _{ }.
12.2. A classification of the structures in \Mod^{ }_{\Uppsi} up to isomorphism
12.3. The invariant universality of \embeds^{ }_{\CT}
12.4. More absoluteness results
Chapter 13. An alternative approach
13.1. Completeness
13.2. Invariant universality
Chapter 14. Definable cardinality and reducibility
14.1. Topological complexity
14.2. Absolutely definable reducibilities
14.3. Reducibilities in an inner model
Chapter 15. Some applications
15.1. \bSigma¹₂ quasi-orders
15.2. Projective quasi-orders
15.3. More complex quasi-orders in models of determinacy
15.4. \Ll(\R)-reducibility
Chapter 16. Further completeness results
16.1. Representing arbitrary partial orders as embeddability relations
16.2. Other model theoretic examples
16.3. Isometry and isometric embeddability between complete metric spaces of density character
16.4. Linear isometry and linear isometric embeddability between Banach spaces of density
16.5. *Further results on the classification of nonseparable metric and Banach spaces
Indexes
Index
Index
Bibliography
Back Cover.