- Axiomatic theories.
- Theory ZF.
- Well-ordered sets. Ordinals. Transifinite induction.
- Comparison of cardinalities. Cantor-Bernstein theorem. Cantor theorem.
- Hartogs' Theorem. Cardinals. Squares of cardinals.
- Confinality. Singular and regular cardinals.
- The sets Z, Q, R. Continuum hypothesis.
- Finite and D-finite sets.
- Axiom of choice, Zermelo theorem, Zorn lemma.
- Cardinal arithmetic. Powers of cardinals. Generalized Continuum hypothesis (GCH).
- Models of first order theories.
- Notations of formulas in ZF. Provability predicate.
- Truth in a model. Consistency and model existence axioms.
- Transitive classes. Extensionality.
- Absolute formulas. Operations defined by formulas.
- Examples of absolute formulas and operations. Goedel operations.
- Almost universal classes. Sufficient conditions to get a model of ZF.
- Regularity axiom (AR). Von Neumann's universum. Relative consistency of (AR).
- Goedel operations and models of ZF.
- Constructive sets and constructivity axiom (V=L).
- Relative consistency of V=L.
- Consistency of the Axiom of Choice.
- Isomorphism theorem. Reflexivity principle.
- Consistency of GCH.
- Complete Boolean algebras.
- Generic sets and Boolean valued models of ZF.
- Independency of V=L.
- Independency of GCH.