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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Main Authors: Andretta, Alessandro, Ros, Luca Motto
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2022
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Embeddings (Mathematics)
Mathematical logic and foundations > Set theory > Descriptive set theory. msc
Mathematical logic and foundations > Set theory > Determinacy principles. msc
Mathematical logic and foundations > Set theory > Inner models, including constructibility, ordinal definability, and core models. msc
Mathematical logic and foundations > Set theory > Ordinal and cardinal numbers. msc
Mathematical logic and foundations > Set theory > Other notions of set-theoretic definability. msc
Set theory
Topological spaces
non-separable Banach spaces
uncountable structures
Generalized descriptive set theory
<inline-formula content-type="math/mathml"> κ \kappa </inline-formula>-Souslin sets
infinitary logics
(bi-)embeddability
non-separable metric spaces
determinacy
ISBN:9781470452735, 1470452731
ISSN:0065-9266, 1947-6221
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Abstract We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case
AbstractList We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case
View the abstract.
Author Ros, Luca Motto
Andretta, Alessandro
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Keywords non-separable Banach spaces
uncountable structures
Generalized descriptive set theory
<inline-formula content-type="math/mathml"> κ \kappa </inline-formula>-Souslin sets
infinitary logics
(bi-)embeddability
non-separable metric spaces
determinacy
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Language English
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Notes Includes bibliographical references (p. 185-189)
May 2022, volume 277, number 1365 (sixth of 6 numbers)
OCLC 1343248959
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Snippet We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case
View the abstract.
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SubjectTerms Embeddings (Mathematics)
Mathematical logic and foundations -- Set theory -- Descriptive set theory. msc
Mathematical logic and foundations -- Set theory -- Determinacy principles. msc
Mathematical logic and foundations -- Set theory -- Inner models, including constructibility, ordinal definability, and core models. msc
Mathematical logic and foundations -- Set theory -- Ordinal and cardinal numbers. msc
Mathematical logic and foundations -- Set theory -- Other notions of set-theoretic definability. msc
Set theory
Topological spaces
TableOfContents 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
Title Souslin quasi-orders and bi-embeddability of uncountable structures
URI https://www.ams.org/memo/1365/
https://cir.nii.ac.jp/crid/1130292546417246623
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Volume 277
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