Contents

• A. Definition of a Formal System

• B. An Example from Group Theory

• C. Representation and Interpretation

• D. Some Semiotical Concepts. The U-Language

• E. An Attempt at Mathematical Grammatics

• F. Semiotical Aspect of a Formal System. The A-Language

• G. Modifications of a Formal System

• H. The System G

Contents

• A. Preliminary Definitions and Notation

• B. Informal Discussion

• C. Classical Form of the Rules

• D. The Systems LA (G) and LC (G)

• E. Some Preliminary Theorems

• F. The Technique of Elementary Derivations. Decidability

• G. The Elimination Theorem

• I. The Natural System T

• J. Equivalent Propositional Algebras. Systems HA and HC

• K. Concluding Remarks

Contents

• A. Preliminary Analysis

• B. Conventions of the B-Language

• C. Rules for Terms and Propositions

• D. The Systems LA* and LC*

• E. Theorems on Extensions

• F. Basic Theorems of the LA* and LC* Systems

• G. The Systems TA*, TC*.

• H. The Predicate Calculus

Contents

• A. Preliminary Analysis

• B. An Example from Number Theory

• C. Formulation of the Rules

• D. Fundamental Theorems

• E. The Natural Systems T

• F. The Propositional Algebras

• G. Concluding Remarks

Contents

• A. Analysis of Necessity

• B. The L-System for Necessity

• C. The T and H Systems for Necessity

• D. Discussion of Possibility