Lattice theory

Garrett Birkhoff

The purpose of the third edition is threefold: to make the deeper ideas of lattice theory accessible to mathematicians generally, to portray its structure, and to indicate some of its most interesting applications. This 1996 reprint includes expanded and updated Additional References.

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Table of contents :
Cover……Page 1
Title page……Page 3
Copyright……Page 4
Preface to the 2nd edition……Page 5
TABLE OF CONTENTS……Page 7
FOREWORD ON ALGEBRA……Page 9
FOREWORD ON TOPOLOGY……Page 12
CHAPTER I. PARTIALLY ORDERED SETS……Page 17
CHAPTER II. LATTICES……Page 32
CHAPTER III. CHAINS AND CHAIN CONDITIONS……Page 47
CHAPTER IV. COMPLETE LATTICES……Page 65
CHAPTER V. MODULAR LATTICES……Page 81
CHAPTER VI. APPLICATIONS TO ALGEBRA……Page 101
CHAPTER VII. SEMI-MODULAR LATTICES……Page 116
CHAPTER VIII. COMPLEMENTED MODULAR LATTICES……Page 130
CHAPTER IX. DISTRIBUTIVE LATTICES……Page 149
CHAPTER X. BOOLEAN ALGEBRAS……Page 168
CHAPTER XI. APPLICATIONS TO SET THEORY……Page 188
CHAPTER XII. APPLICATIONS TO LOGIC AND PROBABILITY……Page 204
CHAPTER XIII. LATTICE-ORDERED SEMIGROUPS……Page 216
CHAPTER XIV. LATTICE-ORDERED GROUPS……Page 230
CHAPTER XV. VECTOR LATTICES……Page 254
CHAPTER XVI. ERGODIC THEORY……Page 275
Bibliography……Page 288
Subject index……Page 292
Author index……Page 296
Colloquium Publications……Page 300