Electronic ISBN:  9780821876923 
Product Code:  CONM/104.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 

Book DetailsContemporary MathematicsVolume: 104; 1990; 176 ppMSC: Primary 03; 18;
Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from GabrielUlmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2categorical in nature; the authors cover some aspects of 2category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given.
Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2categorical methods, and a useful tool for studying toposes and other categories. 
Table of Contents

Chapters

Introduction

Chapter 1: Preliminaries

Chapter 2: Accessible categories and functors

Chapter 3: Sketches and logic

Chapter 4: Sketching accessible categories

Chapter 5: Limits and colimits of accessible categories

Chapter 6: Limits and colimits in accessible categories

References

Index

Glossary of notation


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Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from GabrielUlmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2categorical in nature; the authors cover some aspects of 2category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given.
Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2categorical methods, and a useful tool for studying toposes and other categories.

Chapters

Introduction

Chapter 1: Preliminaries

Chapter 2: Accessible categories and functors

Chapter 3: Sketches and logic

Chapter 4: Sketching accessible categories

Chapter 5: Limits and colimits of accessible categories

Chapter 6: Limits and colimits in accessible categories

References

Index

Glossary of notation