**Contemporary Mathematics**

Volume: 752;
2020;
207 pp;
Softcover

MSC: Primary 03; 28; 05;

**Print ISBN: 978-1-4704-4332-0
Product Code: CONM/752**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

**Electronic ISBN: 978-1-4704-5609-2
Product Code: CONM/752.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

# Trends in Set Theory

Share this page *Edited by *
*Samuel Coskey; Grigor Sargsyan*

This volume contains the proceedings of Simon
Fest, held in honor of Simon Thomas's 60th birthday, from September
15–17, 2017, at Rutgers University, Piscataway, New Jersey.

The topics covered showcase recent advances from a variety of main
areas of set theory, including descriptive set theory, forcing, and
inner model theory, in addition to several applications of set theory,
including ergodic theory, combinatorics, and model theory.

#### Readership

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

# Table of Contents

## Trends in Set Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- The open dihypergraph dichotomy and the second level of the Borel hierarchy 112
- An introduction to combinatorics of determinacy 2132
- 1. Introduction 2132
- 2. Partition Properties 2233
- 3. Good Coding of Functions 2738
- 4. Reasonableness at 𝜔₁ 3243
- 5. Kunen Functions and Partition Properties at 𝜔₂ 4253
- 6. Failure of the Strong Partition Property at 𝜔₂ 5364
- 7. 𝐿(\reals) as a Symmetric Collapse Extension of \HOD 6071
- 8. The Vopénka Forcing 6879
- Acknowledgements 7485
- References 7485

- Isomorphism and weak conjugacy of free Bernoulli subflows 7788
- Distance from marker sequences in locally finite Borel graphs 89100
- The Ultrapower Axiom 93104
- Quasi-invariant measures for continuous group actions 113124
- An example of a new simple theory 121132
- 1. Notation and preliminaries 122133
- 2. Construction 125136
- 3. A non-saturation result for \tsf 130141
- 4. \tsf is explicitly simple 133144
- 5. A saturation result for \tsf 138149
- 7. Consequences for Keisler’s order 145156
- Appendix: perfect ultrafilters for uncountable 𝜃 146157
- Appendix: non-saturation for 𝑇_{𝑘+1,𝑘} and uncountable 𝜃 148159
- Acknowledgments 150161
- References 150161

- A brief introduction to amenable equivalence relations 153164
- Singularizing cardinals 165176
- A brief account of recent developments in inner model theory 175186
- A descriptive construction of trees and Stallings’ theorem 191202
- Back Cover Back Cover1222