Entry requirements

Mathematics, 60 ECTS credits including

Logic MN2 and Algebra MN3.

Aims

To provide basic and deeper knowledge of model theory and of set theory.

Content

Basic model theory: Structure, substructure,

elementary substructure. Methods for constructing

models: Elementary extension, Skolem functions,

ultra products. Model completeness, quantifier

elimination. Basic set theory: The axioms of

Zermelo-Fraenkel set theory (ZF), ordinal

numbers, cardinal numbers, the reflection

principle, Gödel's universe L of definable sets,

proof that the generalised continuum hypothesis

is consistent relative to ZF. Large cardinals,

incompatibility of the existence of measurable

cardinals and the contructibility axiom (V=L).

Instruction

Lectures.

Assessment

Written and, possibly, oral examination at the

end of the course. Compulsory hand-in assignments

may occur during the course.