Ideas from 'works' by Gerhard Gentzen [1938], by Theme Structure

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5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Gentzen introduced a natural deduction calculus (NK) in 1934 [Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The inferential role of a logical constant constitutes its meaning [Hanna]
The logical connectives are 'defined' by their introduction rules
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Musgrave]