Advanced Mathematical Logic 2011/12
A semestral course at the Faculty of Informatics,
Vienna University of Technology,
in the winter term of 2011/12.
Lecturer: Libor Behounek,
course code: 185.A09,
type: VU Lecture and Exercise,
semester hours: 2.0,
EC credits: 3.0.
The course was given in English, in a block mode,
consisting of 7 lectures of 2-3 full hours.
The credits were given based on a test after the final lecture
(also taking into account the mid-term test and homework exercises).
Aim
The aim of the course was to acquaint the students with selected concepts
and methods of mathematical logic and metamathematics, including
the completeness proof for first-order classical logic,
basic model theory,
Gödel's incompleteness theorems,
and the (un)decidability of logical theories.
Syllabus
Syntax and semantics of classical first order logic:
Formula, proof, theory,
first-order structure, model,
syntactic and semantic completeness of theories
Completeness of classical first-order logic:
Henkin completion, compactness, Löwenheim-Skolem theorem
Formal arithmetic:
True arithmetic, Peano and Robinson arithmetic,
standard and non-standard models
(In)completeness and (un)decidability of theories:
Models of computing,
decidable theories, quantifier elimination,
Gödel’s incompleteness theorems.
Study materials
(Updated) handouts for the lectures (PDF):