Logic II is a second level logic course, giving an introduction to major topics of modern mathematical logic. It consists of three main parts:
- axiomatic foundations: Zermelo–Fraenkel set theory, and the development of mathematics therein, including ordinals, cardinals, transfinite recursion, the axiom of choice and its applications, and first independence results
- model theory: structures and isomorphisms, elementary equivalence and embeddings, the Löwenheim–Skolem theorems, categoricity, back-and-forth arguments, and applications/examples including non-standard analysis
- computability and incompleteness: models of computability; (un)decidability and (un)computability; coding of logic, and Gödel’s incompleteness theorems.
The course literature is R. Cori, D. Lascar, 2001, Mathematical logic, a course with exercises, Part II: Recursion Theory, Gödel’s Theorems, Set Theory, Model Theory (Oxford University Press); SU library details.
The main prerequisite course is MM5024 (Mathematics III — Logik) or equivalent; precise prerequisites, full kursplan etc. are here.
Please note that self-enrollment on the course page is not the same as course registration in Ladok.
- Teacher: Peter LeFanu Lumsdaine