Course: M69, Introduction to Mathematical Logic Instructor: Schedule: MWF 1:45-2:50 Objective: As the title of the class suggests, I will go through the bare essentials of mathematical logic and foundations of mathematics. The people leaving the class will understand from set theory: what cardinalities are, that there are different infinite cardinalities and in particular the set of all natural numbers and the set of all real numbers have different cardinality from proof theory: what formal languages, formal theories and formal proofs are, and that arithmetic and set theory can be formalized. I will prove Godel's First Incompleteness Theorem: there are arithmetic statements that cannot be proved or disproved in Peano Arithmetic. from model theory: what models of theories are, and that one theory can have many different models. I will prove Godel's Completeness Theorem: every theory containing no contradictions has a model. from recursion theory: what recursive functions and Turing machines are, and what Church's Thesis means. Prerequisites: Everyone familiar with basic notions of abstract mathematics is welcome. Text: Herbert Enderton: A Mathematical Introduction to Logic, Academic Press 1972. I will not necessarily follow the book to the letter. Exams, etc: Homework assignments every week, one midterm and final. I will emphasize independent work and the final exam.