Model Theory
Syllabus, Master's level, 1MA086
This course has been discontinued.
- Code
- 1MA086
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 29 May 2013
- Responsible department
- Department of Mathematics
Entry requirements
120 credit points with the courses Algebraic Structures and Logic II.
Learning outcomes
In order to pass the course (grade 3) the student should be able to
- construct models using ultra-products;
- apply the compactness theorem in the construction of theories and models;
- determine whether two models are elementarily equivalent;
- use methods from the course to show that some theories have quantifier elimination;
- characterise theories with a unique infinite countable model;
- given a model theoretic property, decide whether a concrete structure has this property or not, and be able to justify why;
- construct concrete examples to illustrate important model theoretic notions;
- outline proofs of important theorems of the course and explain the main ideas of the proofs;
- give examples of algebraic applications of model theory.
Content
Ultra products. The compactness theorem. Elementary substructures and extensions, categoricity, elimination of quantifiers, types, Stone spaces, algebraic closure in structures. Saturated structures, atomic structures, prime models, omitting types, characterisations of theories with a unique infinite countable model, theories with finitely many infinite countable models, minimal theories, dimension, total categoricity, Steinitz' theorem and its model theoretic version. Introduction to model theoretic stability theory. Applications to algebra.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination combined with assignments given during the course in accordance with instructions at course start.