Simplicity Theory
Byunghan Kim
Abstract
This book is about simple first-order theories. The class of simple theories was introduced by S. Shelah in the early 1980s. Then several specific algebraic structures having simple theories have been studied by leading researchers, notably by E. Hrushovski. In the mid-1990s the author established in his thesis the symmetry and transitivity of non-forking for simple theories and, with A. Pillay, type-amalgamation for Lascar strong types. Since then a great deal of research work on simplicity theory, the study of simple theories and structures has been produced. This book starts with the introd ... More
This book is about simple first-order theories. The class of simple theories was introduced by S. Shelah in the early 1980s. Then several specific algebraic structures having simple theories have been studied by leading researchers, notably by E. Hrushovski. In the mid-1990s the author established in his thesis the symmetry and transitivity of non-forking for simple theories and, with A. Pillay, type-amalgamation for Lascar strong types. Since then a great deal of research work on simplicity theory, the study of simple theories and structures has been produced. This book starts with the introduction of the fundamental notions of dividing and forking, and covers up to the hyperdefinable group configuration theorem for simple theories.
Keywords:
dividing,
forking,
simplicity,
type amalgamation,
group configuration
Bibliographic Information
| Print publication date: 2013 |
Print ISBN-13: 9780198567387 |
| Published to Oxford Scholarship Online: January 2014 |
DOI:10.1093/acprof:oso/9780198567387.001.0001 |
Authors
Affiliations are at time of print publication.
Byunghan Kim, author
Professor of Mathematics, Department of Mathematics, Yonsei University, South Korea
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