How to Learn Mathematical Logic

Study first-order predicate logic: predicates, functions, universal and existential quantifiers, free and bound variables, and translating natural language into formal statements.

Master natural deduction and sequent calculus. Practice constructing formal proofs using inference rules such as Modus Ponens, Modus Tollens, conditional proof, and proof by contradiction.

Study naive and axiomatic set theory (ZFC). Cover the axioms, ordinals, cardinals, Cantor's theorem, the Axiom of Choice, and how set theory provides the foundation for mathematics.

Explore the relationship between formal languages and their interpretations. Study structures, satisfaction, the Compactness Theorem, the Loewenheim-Skolem Theorem, and elementary equivalence.

Learn Turing machines, recursive functions, the Church-Turing thesis, decidable and undecidable problems, the Halting Problem, and reducibility between problems.

Study Goedel numbering, the diagonal lemma, Goedel's Completeness and Incompleteness Theorems, Gentzen's consistency proof, and ordinal analysis of formal systems.

Explore modal logic, intuitionistic logic, non-classical logics, automated theorem proving, formal verification, and connections to computer science, linguistics, and philosophy.