Hilbert systems

A Hilbert system is a formal framework used in logic to prove statements using a set of specific rules and axioms. Think of it as a logical recipe book: starting from basic truths (axioms), you apply systematic rules to derive new truths (theorems). This method ensures that if a statement can be proven within the system, it is logically valid. Hilbert systems are valued for their clarity and minimalism, focusing on proof structure rather than the process of derivation itself. They are fundamental in understanding formal reasoning and underpin many areas of mathematical logic and computer science.