[ Lehrveranstaltungen 185/2 ]
[ AG Theoretische Informatik und Logik ]
[ Fakultät für Informatik ]
[ Technische Universität Wien ]

# 185.332 Mathematical Logic 2, VU 3.0/2.0, SS 2011

Lecturer:
Stefan Hetzl, email: hetzl AT logic.at
This course is an optional course in the
Computer Science Master Study
*Computational Intelligence*
(Wahlfachkatalog *Theoretische Informatik und Logik*)
and belongs to the module *Foundations* of the
European Masters Program in
Computational Logic.

The course will be held in english.

### Content:

The aim of this course is to discuss some of the most central ideas and results of mathematical logic.
The first part of the course is about pure first-order logic and its model theory. It will mainly
consist of proving the completeness, compactness and Löwenheim-Skolem theorems. The second part
will deal with arithmetic and recursion theory leading to Gödel's first incompleteness theorem.
### Prerequisites:

Familiarity with the syntax and semantics of first-order logic (as taught for example in the course
Mathematical Logic 1).
### Schedule:

The course will be held in blocked form from 14th of March until 11th of April.
All lessons will be in the Gödel seminar room, Favoritenstraße 9.

The dates are:
- Monday, 14.3.2011: 16 - 18, course notes
- Wednesday, 16.3.2011: 10 - 13, course notes
- Friday, 18.3.2011: 15 - 18, course notes
- Wednesay, 30.3.2011: 10 - 13, first exercise session, course notes
- Friday, 1.4.2011: 16 - 18, course notes
- Monday, 4.4.2011: 16 - 18, second exercise session
- Wednesday, 6.4.2011: 10 - 13, course notes
- Friday, 8.4.2011: 15 - 18, course notes
- Monday, 11.4.2011: 16 - 19, third exercise session

### Exam:

A written exam will be on:
Thursday, 14.4.2011, 14 - 16 in the Gödel seminar room

### Exercises:

### Literature:

**NEW:** The course notes of this summer term as one big pdf file.
In addition, the following introductions to mathematical logic are useful:

- Dirk van Dalen: Logic and Structure, Springer.
- Boolos, Burgess, Jeffrey: Computability and Logic, Cambridge University Press.
- Joseph Shoenfield: Mathematical Logic, AK Peters.

More specialised texts that are recommended for further reading:

- Alexander George, Daniel J. Velleman: Philosophies of Mathematics, Blackwell.
- Wilfrid Hodges: A Shorter Model Theory, Cambridge University Press.
- Gaisi Takeuti: Proof Theory, Elsevier.
- Piergiorgio Odifreddi: Classical Recursion Theory, North Holland.
- Kenneth Kunen: Set Theory, North Holland.

Many of these books are available from the university library.

A website containing links to many
introductory articles about various subjects in mathematical logic.

### Assessment:

The practical part of the course is integrated and will take place in
the form of exercises which should be solved at home and will be discussed
in the course. At the end there will be a final exam.
The overall assessment takes into account the final exam, but
also the exercises and the general participation during the course.

Last Change: 2011-04-08