Foundations

Learn Proof Theory

Proofs treated as mathematical objects with a shape, a size and an ordinal. Covers the sequent calculus and cut elimination as an algorithm, Herbrand's theorem, constructive interpretations, ordinal analysis from Gentzen to the modern programme, and the complexity of proofs themselves.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Proof Theory

Hilbert systems and the deduction theoremThe sequent calculus LKCut elimination as an algorithmThe cost of cut eliminationHerbrand's theoremIntuitionistic logic and BHKThe double-negation translationRealizabilityThe Dialectica interpretationPrimitive recursive arithmeticOrdinal notations below $\varepsilon_0$Assigning ordinals to proofsProof-theoretic ordinalsGoodstein sequences and the hydraThe $\omega$-rule and infinitary proofsBounded arithmeticPropositional proof complexityLinear logic and substructural logics
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Proof Theory exactly where it's useful.

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