# Set Theory and Its Applications

Share this page *Edited by *
*L. Babinkostova; A. E. Caicedo; S. Geschke; M. Scheepers*

This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.

#### Readership

Graduate students and research mathematicians interested in set theory and its modern applications.

# Table of Contents

## Set Theory and Its Applications

- Contents v6 free
- Preface vii8 free
- Past Invited Speakers at BEST ix10 free
- Some Positive Results in the Context of Universal Models 114 free
- A Survey of D-spaces 1326
- Combinatorics of Filters and Ideals 2942
- More Structural Consequences of AD 7184
- 1. Introduction 7184
- 2. Preliminaries 7285
- 3. Cone ultrafilters and ultraproducts. 7790
- 4. Compatibility of constructibility degrees. 8093
- 5. Constructibility degrees and the structure of AD models 8497
- 6. Strong ∞-Borel codes 95108
- 7. Equivalence of AD+ with the closure of the Suslin cardinals below Θ 98111
- 8. Appendix 99112
- References 104117

- αi-selection Principles and Games 107120
- Jensen's Diamond Principle and Its Relatives 125138
- Paracompactness and Normality in Box Products: Old and New 157170
- Some Problems and Techniques in Set-Theoretic Topology 183196
- Menger's and Hurewicz's Problems: Solutions from "The Book" and Refinements 211224
- A Trichotomy Theorem in Natural Models of AD+ 227240
- The Coinitialities of Efimov Spaces 259272
- Uniforming n-place Functions on Well Founded Trees 267280
- A Classical Proof of the Kanovei-Zapletal Canonization 281294
- Lords of the Iteration 287300