Foundations

Learn Mathematical Logic

From truth tables to Gödel and Turing: propositional and predicate logic, normal forms and resolution, natural deduction, the completeness and compactness theorems, the incompleteness theorems, and the limits of computation.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

22 lessons in Mathematical Logic

Propositional logic & truth tablesLogical equivalenceNormal forms: CNF & DNFSatisfiability, validity & resolutionPredicate logic & quantifiersFirst-order structures & modelsNatural deduction & formal proofWhat a proof isDirect proof & working with definitionsProof by contrapositiveProof by contradictionProof by cases & without loss of generalityMathematical inductionStrong induction & well-orderingExistence & uniqueness proofsDisproof by counterexampleReading proofs criticallySoundness & the completeness theoremCompactness & Löwenheim–SkolemGödel's incompleteness theoremsTuring machines & computabilityThe halting problem & undecidability
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 day its model predicts you would forget it. A short placement check finds what you already know, so you start Mathematical Logic exactly where it's useful.

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