: A more abstract system that facilitates metamathematical analysis. It is the primary tool for proving the field's most important theorems, such as consistency and decidability. 2. Core Concepts
: Gentzen's most famous result, which states that any proof containing a "cut" (a detour or lemma) can be transformed into a cut-free (or normal) form. Structural Proof Theory
: Designed to mirror "natural" human reasoning by using rules for introducing and eliminating logical constants. : A more abstract system that facilitates metamathematical
The field is defined by two primary systems developed by in the 1930s: Structural Proof Theory
Structural proof theory is not merely theoretical; it serves as a foundation for several modern fields: