Structural Proof Theory -

: It provides the tools to demonstrate that a logical system is consistent (i.e., it cannot prove a contradiction) by showing that no proof of an "empty" or false statement exists.

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: : It provides the tools to demonstrate that

: A direct consequence of cut-elimination, this property ensures that a normal proof of a formula only contains subformulas of Structural Proof Theory