Structure And Randomness In Computability And Set Theory

This volume explores the interface between set theory and computability, including Borel equivalence, Borel reducibility, and Borel determinacy, as well as algorithmic randomness and dimension, Ramsey sets, and Ramsey spaces.

Format: Hardback
Length: 388 pages
Publication date: 29 October 2020
Publisher: World Scientific Publishing Co Pte Ltd

This volume presents some exciting new developments occurring on the interface between set theory and computability, as well as their applications in algebra, analysis, and topology. These include effective versions of Borel equivalence, Borel reducibility, and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.

The study of the relationship between set theory and computability has produced a wealth of exciting developments in recent years. This volume showcases some of the most notable advancements in this field, including effective versions of Borel equivalence, Borel reducibility, and Borel determinacy. These concepts are fundamental to understanding the complexity of mathematical structures and have numerous applications in areas such as algebra, analysis, and topology.

In addition to these theoretical developments, this volume also explores the applications of set theory and computability in areas such as algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Algorithmic randomness is a crucial concept in computer science and mathematics, as it allows for the generation of random numbers and sequences that are useful in various applications, including simulations, encryption, and data analysis. Dimension is a fundamental concept in topology, which studies the properties of spaces that can be embedded in Euclidean space. Ramsey sets and Ramsey spaces are important examples of spaces that exhibit certain structural properties, such as the existence of infinite Ramsey trees, which have applications in graph theory and combinatorics.

The annual Southeastern Logic Symposium, supported by the National Science Foundation (NSF), is a prominent forum for discussing these and other topics related to set theory and computability. The symposium brings together researchers from around the world to share their latest findings and exchange ideas. The 2017 symposium, held in Atlanta, Georgia, featured a wide range of presentations and discussions on these and other topics, including the use of set theory and computability in artificial intelligence, computer science, and mathematics education.

Overall, this volume presents a comprehensive overview of the latest developments in the interface between set theory and computability, as well as their applications in various fields. It is an essential resource for researchers and students interested in this area of study.

Weight: 712g
Dimension: 158 x 235 x 30 (mm)
ISBN-13: 9789813228221