Wahlmodul on Model Theory
Syllabus
This series of lectures will give an introduction to model theory, a branch of mathematical logic concerned with first-order statements, i.e. statements in languages allowing quantification over elements of a given structure.We will introduce the formalism of model theory, including (first-order) lnguges, structures, theories and models, and present the main basic notions and results in model theory: elementary extensions, types and saturated structures, compactness, caegoricity, model completeness and quantifier elimination.
The lectures will also be oriented toward applied model theory, i.e. the use of model theory in order to study algebraic structures such as groups and fields, possibly valued, as well as valued fields. A particularly important model theoretic tool in this respect is elimination theory. These applications will mainly be visited in the exercise sessions.
The main reference for the lectures is C. N. Delzell and A. Prestel's Mathematical Logic and Model Theory, Brief Introduction, mainly Chapters 2 and 3.
Tutorium
The exercises will take place every two weeks at a date to be agreed upon during the first lecture on April, 14th. Homepage of the tutorium.References and notes
I will post some notes and further references pertaining to questions that may come up in class here.Letzte Änderung: