Souslin quasi-orders and bi-embeddability of uncountable structures / Alessandro Andretta, Luca Motto Ros.

Format:

Book

Author/Creator:

Andretto, Alessandro, author.

Motto Ros, Luca, author.

Series:

Memoirs of the American Mathematical Society ; no. 1365.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 1365

Language:

English

Subjects (All):

Logic.

Number theory.

Algebra.

Physical Description:

vii, 189 pages ; 26 cm.

Place of Publication:

Providence, RI : AMS, American Mathematical Society, [2022]

Contents:

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 t bi-embeddability

1.6 Organizations 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 determinancy

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 2K

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 K-spaces, K-analytic quasi-orders, and spaces of codes

7.1 K-analytic sets

7.2 Spaces of type K 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. K-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 determinancy

Chapter 10. The main construction

10.1 The combinatorial trees G0 and G1

10.2 The combinatorial trees GS

Chapter 11. Completeness

11.1 Faithful representations of K-Souslin quasi-orders

11.2 The quasi-order ≤max and the reduction T

11.3 Reducing ≤Kmax to KCT

11.4 Some absoluteness results

Chapter 12. Invariant universality

12.1 An LK+K-sentence describing the structures GS.

12.2 A classification of the structures in Mod K up to isomorphism

12.3 The invariant universality of KCT

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 12 quasi-orders

15.2 Projective quasi-orders

15.3 More complex quasi-orders in models of determinancy

15.4 L(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 Banach spaces of density K

16.4 Linear isometry and linear isometric embeddability between Banach spaces of density K

16.5 *Further results on the classification of nonseparable metric and Banach spaces

Indexes

Concepts

Symbols

Bibliography

Notes:

"May 2022, volume 277, number 1365 (sixth of 6 numbers)."

Includes bibliographical references (pages 185-189) and index.

ISBN:

1470452731

9781470452735

OCLC:

1314257331