Teaching
Contents
The course gives an introduction into mathematical logic with special focus on applications in computer science. It presents first propositional logic, then first-order logic and treats especially resolution as a formal proof system, a calculus that plays a central role in computer science. Additionally the course presents modal logic and their applications to formal verification, as well as the automata theoretic approach to their algorithmics.
StuIP contains regularly updated lecture notes.
Course
Tuesday, Wednesday 10:00-12:00 in HS12 (IM).
Übungen
Azzas Gaysin Thursday 14:00-16:00 and 16:00-18:00 im SR001 (ITZ).
New exercise sheets Tuesday afternoon on StudIP.
Literatur
Ebbinghaus, Flum, Thomas, Mathematical Logic, 1994 Springer
Ebbinghaus, Flum, Thomas, Einführung in die mathematische Logik, 2018, Springer
Ebbinghaus, Flum, Finite Model Theory, 1994, Springer
Kreutzer, Kühling, Logik für Informatiker, here
Thomas, Languages, Automata and Logic, pdf
Schöning, Logik für Informatiker, here
Baier, Katoen, Principles of Model Checking, pdf
Contents
Vector spaces over a given field are determined (up to isomorphism) by their dimension. Algebraically closed fields with a given characteristic are determined by their transcendence degree. In particular, these theories have exactly one model in each uncountable cardinality. What do these theories have in common that explains this similar behavior? The course gives an introduction to stability theory. In particular, it introduces a general notion of dimension. The central goal of the course is to prove Morley’s theorem: if a theory has exactly one model of some uncountable cardinality, then this holds for all uncountable cardinalities.
The course is a continuation of last semster's course Model Theory. With some extra effort the course is accessible to students with only some good background in first-order logic.
Lectures
Wednesday 12:00-14:00 in HS12 (IM)
Exercises
By Azza Gaysin Wednesday 14:00-16:00 in HS12 (IM)
Literature
Tent, Ziegler, A Course in Model Theory (Lecture Notes in Logic), Cambridge University Press, 2012.
Marker, Model Theory : An Introduction, Springer Graduate Texts in Mathematics 217, 2010. Here.
This is an advanced seminar joint with the chair of Pure Mathematics. Advanced students who wish to deepen their knowledge in mathematical logic and/or complexity theory can give talks on jointly chosen and jointly elaborated topics.