Foundations

Learn Model Theory

Elementary equivalence against isomorphism, elementary substructures and the Tarski-Vaught test, Ehrenfeucht-Fraisse games and the limits of first-order expression, quantifier elimination in dense orders, Presburger arithmetic, algebraically closed and real closed fields, o-minimality, type spaces, omitting types, saturation, Ryll-Nardzewski, Vaught's two-model theorem, Fraisse limits, the Rado graph and the zero-one law, strongly minimal sets and indiscernibles.

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

What you'll learn

18 lessons in Model Theory

Elementary equivalence and isomorphismElementary substructures and the Tarski-Vaught testEhrenfeucht-Fraisse gamesWhat first-order logic cannot sayQuantifier eliminationPresburger arithmetic and decidable theoriesAlgebraically closed fieldsReal closed fields and the projection theoremO-minimalityTypes and the Stone spaceIsolated types, atomic models and omittingSaturation and homogeneityCountable categoricity and Ryll-NardzewskiVaught's theorem: never exactly twoFraisse limits and amalgamationThe Rado graph and the zero-one lawStrongly minimal sets and Morley rankIndiscernibles and Ehrenfeucht-Mostowski models
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 Model Theory exactly where it's useful.

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