Learning Path — Model Theory
Suggested preparation for Model Theory. Choose an entry point that fits your preparation.
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Entry / bridge route · Additional preparation for research reading · All paths
Entry / bridge route
Proofs & Mathematical Writing
Read quantified statements; write direct, contrapositive, contradiction and induction arguments.
Book of Proof — Richard Hammack. Direct open PDF
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You can explain the quantifiers in a statement and write these forms of proof without relying on a worked solution.
Mathematical Logic & Computability
Use first-order syntax, semantics, quantifiers and proof systems.
forall x: Calgary — P. D. Magnus, Tim Button, Aaron Thomas-Bolduc and Richard Zach, with contributors. Open online text / archive
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You can distinguish validity from derivability and explain the relevant soundness and completeness statements.
Set Theory
Understand orders, cardinality, ordinals and the role of axioms.
Set Theory: An Open Introduction — Tim Button. Open online text / archive
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You can distinguish countability, cardinality and order type; forcing-specific preparation is a separate step.
Linear Algebra
Work with vector spaces, bases, linear maps, kernels, rank and eigenvalues.
Linear Algebra — Jim Hefferon. Open online text / archive
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You can prove rank–nullity, change bases and distinguish diagonalizable maps from general linear maps.
Abstract Algebra & Galois Theory
Use groups, rings, ideals, quotient constructions and field extensions.
Abstract Algebra: Theory and Applications — Thomas W. Judson. Open online text / archive
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You can construct quotient groups and rings correctly and state the assumptions of the isomorphism theorems.
Model Theory
Study structures, elementary equivalence, compactness and types.
Lecture Notes — Model Theory (Math 411) — Anand Pillay. Direct open PDF
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You can use compactness and elementary embeddings in examples; stability or classification theory may still need a bridge.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.