Logic II
Logic II is a second tier logic course, on the advanced level, which gives an introduction to modern mathematical logic. It includes Gödel incompleteness theorems, computability theory, model theory, nonstandard analysis, axiomatic set theory, ordinal and cardinal numbers, equivalents of the axiom of choice.
The course covers:
- Fundamentals and set theory: The Zermelo-Fraenkel axioms of set theory, elementary theory for cardinals and ordinals. Equivalent formulations of the axiom of choice and its applications in analysis and algebra.
- Structures and models: Isomorphisms and embeddings, complete theories, elementary equivalence and elementary embedding, Löwenheim-Skolem’s theorems, categoricity, applications on algebraic theories and non-standard analysis.
- Computability and incompleteness: Models of computation, classes of computable functions, decidable and irreversible problems, Gödel coding and Gödel’s incompleteness theorem.
The course consists of one element.
Teaching Format
Instruction consists of lectures, computer laborations and exercises.
Assessment
The course is assessed through written examination.
Examiner
The schedule will be available no later than one month before the start of the course.
We do not recommend print-outs as changes can occur. At the start of the course,
your department will advise where you can find your schedule during the course.
Note that the course literature can be changed up to two months before the start of the course.
R. Cori, D. Lascar; Recursion Theory, Godel's Theorems, Set Theory, Model Theory. Oxford university press.
Course reports are displayed for the three most recent course instances.
