## Table of contents for Principles of mathematical logic / D. Hilbert and W. Ackermann ; translated from the German by Lewis M. Hammond, George G. Leckie, F. Steinhardt ; edited and with notes by Robert E. Luce.

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I. THE SENTENTIAL CALCULUS

1. Introduction of the Fundamental Logical Connectives  3
2. Equivalence; Dispensability of Fundamental Connec-
tives                                           5
3. Normal Form for Logical Expressions                 11
4. Characterization of Logically True Combinations of
Sentences                                        13
5. The Principle of Duality                            15
6. The Disjunctive Normal Form for Logical Expressions  17
7. The Totality of Combinations which Can be Formed
from Given Elementary Sentences                  18
8. Supplementary Remarks on the Problem of Universal
Validity and Satisfiability                      21
9. Systematic Survey of All the Deductions from Given
Axioms                                           23
10. The Axioms of the Sentential Calculus              27
11. Examples of the Proof of Theorems from the Axioms 30
12. The Consistency of the System of Axioms         38
13. The Independence and Completeness of the System  40

II. THE CALCULUS OF CLASSES (MONADIC PREDICATE CALCULUS)

1. Reinterpretation of the Symbolism of the Sentential
Calculus                                         44
2. The Combination of the Calculus of Classes with the
Sentential Calculus                              47
3. Systematic Derivation of the Traditional Aristotelian
Inferences                                       48

III. THE RESTRICTED PREDICATE CALCULUS

1. Inadequacy of the Foregoing Calculus                55
2. Methodological Basis of the Predicate Calculus    56
3. Preliminary Orientation on the Use of the Predicate
Calculus                                         61
4. Precise Notation for the Predicate Calculus       65
5. The Axioms of the Predicate Calculus                67
6. The System of Universally Valid Formulas            71
7. The Rule of Substitution; Construction of the Contra-
dictory of a Formula                             79
8. The Extended Principle of Duality; Normal Forms   81
9. Consistency and Independence of the System of Axioms 87
10. The Completeness of the Axiom System               92
11. Derivation of Consequences from Given Premises;
Relation to Universally Valid Formulas          101
12. The Decision Problem                              112

IV. THE EXTENDED PREDICATE CALCULUS

1. The Predicate Calculus of Second Order             125
2. Introduction of Predicates of Second Level; Logical
Treatment of the Concept of Number              135
3. Representation of the Fundamental Concepts of Set
Theory in the Extended Calculus                 139