Souslin quasi-orders and bi-embeddability of uncountable structures
We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case
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| Hlavní autoři: | , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Providence, Rhode Island
American Mathematical Society
2022
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| Vydání: | 1 |
| Edice: | Memoirs of the American Mathematical Society |
| Témata: | |
| ISBN: | 9781470452735, 1470452731 |
| ISSN: | 0065-9266, 1947-6221 |
| On-line přístup: | Získat plný text |
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- Introduction -- Preliminaries and notation -- The generalized Cantor space -- Generalized Borel sets -- Generalized Borel functions -- The generalized Baire space and Baire category -- Standard Borel <inline-formula content-type="math/mathml"> κ \kappa </inline-formula>-spaces, <inline-formula content-type="math/mathml"> κ<!-- κ --> \kappa </inline-formula>-analytic quasi-orders, and spaces of codes -- Infinitary logics and models -- <inline-formula content-type="math/mathml"> κ<!-- κ --> \kappa </inline-formula>-Souslin sets -- The main construction -- Completeness -- Invariant universality -- An alternative approach -- Definable cardinality and reducibility -- Some applications -- Further completeness results -- Indexes
- 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
- 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