His main work was on the foundations of mathematics, in proof theory.

This idea led to the study of proof theory.

He is best known for his work on proof theory and the foundations of natural deduction.

The field of proof theory studies formal proofs and their properties.

In parallel, the foundations of structural proof theory were being founded.

They occur naturally in proof theory, and were first noticed there (before receiving a name).

This is especially important when using proof theory (as often desired) for automated deduction.

This theorem also has important roles in constructive mathematics and proof theory.

These functions are also important in proof theory.

These finite deductions themselves are often called derivations in proof theory.

He was one of the founders of proof theory and mathematical logic.

It overlaps with proof theory and effective descriptive set theory.

Proof theory is the study of formal proofs in various logical deduction systems.

Modern proof theory treats proofs as inductively defined data structures.

Beyond programming languages, the lambda calculus also has many applications in proof theory.

In proof theory, the turnstile is used to denote "provability".

He made important contributions to proof theory.

Proof theory - The study of deductive apparatus.

Thus the proof theory of first-order logic becomes more complicated when empty structures are permitted.

Being semantically constructed, as yet computability logic does not have a fully developed proof theory.

They are the model theory of truth and the proof theory of truth.

Several important logics have come from insights into logical structure arising in structural proof theory.

Gentzen's theorem spurred the development of ordinal analysis in proof theory.

The field of mathematics known as proof theory studies formal axiom systems and the proofs that can be performed within them.

This corollary is sometimes expressed by saying that second-order logic does not admit a complete proof theory.