What you'll learn

36 lessons in Set theory & foundations

Russell's paradox & ZFCCardinalityOrdinals & well-orderingAxiom of ChoiceCardinal arithmeticRussell, Gödel, and limits of formal systemsTransfinite induction & recursionVon Neumann ordinalsLarge cardinalsForcing (intro)Axiom of Foundation & cumulative hierarchyInner models & Gödel's LMartin's axiom & forcing variantsDescriptive set theoryDeterminacyProof of Cantor's diagonalProof: $|\mathbb Q| = |\mathbb N|$Russell's paradox in detailFirst-order logic: syntaxFirst-order logic: semanticsSoundness & the completeness theoremThe compactness theoremLöwenheim–Skolem theoremsModel theory connectionTuring machines & computabilityThe halting problem & undecidabilityThe EntscheidungsproblemCraig's interpolation theoremGödel's incompleteness theoremsTuring degrees & the arithmetical hierarchyTypes, saturation & categoricityUltraproducts & Łoś's theoremProof theory & cut eliminationThe lambda calculusNonstandard analysis & the hyperrealsReverse mathematics

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 Set theory & foundations exactly where it's useful.

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