Hilbert system

Summary

A Hilbert system is a proof system with many axiom schemas and very few rules of inference, often only modus ponens. A proof is a finite list of formulas in which each formula is an axiom, a hypothesis, or follows from earlier ones by a rule. Hilbert systems are simple to describe and to reason about, which makes them the standard tool for results about provability. They are named after David Hilbert.