These are lecture notes from an introduction to axiomatic set theory taught by Scott Weinstein in the spring of 2009, typed up by me and Vilhelm Sjoberg. I make no guarantees whatsoever as to their completeness or correctness! A PDF for each individual lecture is provided below; you can also download all the lecture notes in one big PDF.

 1/21 Well orderings 1/26 Ordinals, transfinite induction 1/28 Transfinite recursion, cardinals 2/2 Cardinals (Axiom of Choice, cardinality, normal functions, cofinality, cardinal arithmetic) 2/4 More cardinals (regularity, the Continuum Hypothesis, Koenig's theorem) 2/9 The real line (partial isomorphisms, Cantor's back-and-forth theorem, uniqueness of the reals, the Cantor set) 2/11 The real line, part II (perfect sets, Cantor-Bendixson theorem) 2/16 Introduction to relative consistency results (Axiom of Regularity, transitive closure, relativization, absoluteness) 2/18 A digression on absoluteness (elementary substructures, Mostowski's Collapsing Lemma, nonstandard (non-well-founded) models, completeness and compactness of first-order logic, Lowenheim-Skolem Theorem, Skolem's paradox) 2/23 Proof of the Lowenheim-Skolem Theorem and related results 2/25 More relative consistency: consistency of ZF - Reg implies consistency of ZF. 3/2 Strongly inaccessible cardinals and ZF. 3/16 Midterm exam review. 3/18 The reflection principle. 3/23 The constructible hierarchy, formal definition (encoding formulas as sets, satisfiability, Delta-1) 3/25 The constructible hierarchy, part II (More Delta-1, absoluteness of L, almost universal, L models ZF) 3/30 The constructible hierarchy, part III (inner models, ZF + (V=L) proves AC) 4/1 The constructible hierarchy, part IV (ZF + (V=L) proves GCH) 4/6 Independence of CH from ZFC (partial orders, filters, P-genericity) 4/8 Independence of CH (cardinal preservation, antichains, ccc, quasi-disjointness) 4/13 Independence of CH (more ccc and preservation of cardinals, P-names) 4/15 Independence of CH (generic extensions, properties of generic extensions, forcing, Truth, Definability) 4/20 Independence of CH (M[G] is a ctm, digression on Kripke-Platek set theory, axiom of Collection, and computability) 4/22 Independence of CH (finish proof that M[G] is a ctm), Ramsey's theorem 4/27 Ramsey cardinals