Libor Behounek - Logic - Teaching - Advanced Mathematical Logic

Advanced Mathematical Logic

A course at the Vienna University of Technology, Faculty of Informatics I taught in 2011 and 2013 (in English, for international students).

  1. Syntax and semantics of classical first order logic: Formula, proof, theory, first-order structure, model, syntactic and semantic completeness of theories, the deduction theorem.
  2. Completeness of classical first-order logic: Henkin completion, Gödel’s completeness theorem, compactness, Löwenheim–Skolem theorem.
  3. Formal arithmetic: True arithmetic, Peano and Robinson arithmetic, standard and non-standard models.
  4. (In)completeness and (un)decidability of theories: Models of computing, decidable theories, quantifier elimination, Gödel’s incompleteness theorems.
Handouts for the lectures (PDFs):