TABLE OF CONTENTS: Preface ix
Chapter 1. Algebra of Classes and Propositional Calculus 1
1.1 Boole 1
1.2 Jevons 10
1.3 Peirce 12
1.4 Schröder 17
Chapter 2. The Theory of Relatives 31
2.1 Introduction 31
2.2 Basic concepts of the theory of relatives 33
2.3 Basic postulates of the theory of relatives 40
2.4 Theory of relatives and model theory 51
2.5 First-order logic of relatives 66
Chapter 3. Changing the Order of Quantifiers 73
3.1 Schröder's proposal 73
3.2 Löwenheim's approach 81
3.3 The problem of expansions 87
3.4 Skolem functions 94
Chapter 4. The Löwenheim Normal Form 107
4.1 The Löwenheim normal form of an equation 107
4.2 Comments on Löwenheim's method 113
4.3 Conclusions 122
Chapter 5. Preliminaries to Löwenheim's Theorem 129
5.1 Indices and elements 129
5.2 Types of indices 132 5.3 Assignments 135
5.4 Types of equations 138
Chapter 6. Löwenheim's Theorem 143
6.1 The problem 143
6.2 An analysis of Löwenheim's proof 148
6.3 Reconstructing the proof 191
Appendix. First-Order Logic with Fleeing Indices 207
A.1 Introduction 207
A.2 Syntax 207
A.3 Semantics 211
A.4 The Löwenheim normal form 217
A.5 Löwenheim's theorem 220
References 227
Index 237
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