18.510 Introduction to Mathematical Logic and Set Theory

Time/place: MWF 2:00 in 2-142

Office hours: Monday 1:00, Tuesday 2:00 in 2-377, or by appointment

Midterm exam during class on Wednesday, October 26; final exam 9:00-11:00 on December 20 in 56-154

Topics: Propositional and predicate logic. Zermelo-Frenkel set theory. Ordinals and cardinals. Axiom of choice and transfinite induction. Elementary model theory: completeness, compactness, and Löwenheim-Skolem theorems. Gödel's incompleteness theorem.

Handouts

• Course information
• Questionnaire
• Playing games with games: the Hypergame paradox, by William Zwicker
• Set theory notes
• Boolean algebra and propositional calculus notes
• Filter notes
• First-order logic notes (handwritten so far)
• Formal proofs and Henkin's proof of completeness (handwritten so far and really sketchy)
• Incompleteness notes
• Inaccessible cardinals and models of ZFC (handwritten so far)