Proof Theory

The branch of mathematical logic that analyses formal proofs as mathematical objects: formal calculi, derivations, proof transformations, consistency, cut-elimination, and measures of proof complexity and constructive content.

Proof theory is the branch of formal logic that studies proofs as formal, syntactic objects: it analyses the structure, transformations, and properties of formal derivations within specified proof systems (e.g., normalization, cut-elimination, decidability, consistency), treating rules, proof transformations and derivability relations as primary objects of investigation rather than model-theoretic