Objectives
Understanding some key tools, techniques and results of model theory.
Contents
In this course we will give a general introduction to the methods and results of classical model theory including games, compactness, the Loewenheim-Skolem theorems, and various preservation theorems, illustrated by examples and applications in algebra and discrete mathematics. Various model theoretic techniques for constructing models will be introduced and applied, such as unions of elementary chains, omitting types construction, ultraproducts and saturated models.
Recommended prior knowledge
We presuppose some (but very little) background knowledge in logic; roughly, what is needed is familiarity with the syntax and semantics of first-order languages. More importantly, we assume that participants in the course possess some mathematical maturity, as can be expected from students in mathematics or logic at a MSc level.
Registration at
Registration for courses is mandatory, but will be done by the Education Service Centre for the 1st year MSc students for courses of the first semester. See also
http://www.student.uva.nl and choose your master and then 'New procedure 'Registration for courses Faculty of Science'.
Format
Lecture Course plus Exercise Sessions.
Study materials
Hodges, Wilfrid,
A shorter model theory,
Cambridge University Press, 1997,
ISBN-13: 978-0-521-58713-6, ISBN-10: 0521587131
Assessment
Homework and/or final examination.
Remarks
See the course website at:
http://staff.science.uva.nl/~yde/teaching/mt
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