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).

Syllabus:

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):

• Handout #1
• Handout #2
• Handout #3
• Handout #4
• Handout #5
• Handout #6
• Handout #7