# Courses Winter Semester 2011-2012

(Diese Seite gibt es auch auf Deutsch.)

- Note: All lectures at the KGRC (apart from
*Introduction to Mathematical Logic*VO + PS, and the Axiomatic Set Theory reading course VO) are given in English, or at least can be given in English if requested.

Information on this page is tentative and subject to change!

See also the course catalogue of the University of Vienna for the 3 mathematics programmes:

Bachelor • Diploma • Master.

Number | Type | Hours (ECTS) | Title | Module | Lecturer | Time | Language |
---|---|---|---|---|---|---|---|

250085 | VO | 4 (6.0) | Introduction to Mathematical Logic | MLOL | Hans Adler | Wed 15:15-16:45, Thu 11:15-12:45 starts 2011-10-06 | Probably in English, following a German book |

250086 | PS | 2 (3.0) | Proseminar to Introduction to Mathematical Logic | MLOL | Peter Holy | Wed 11:15-12:45 starts 2011-10-19 | |

250090 | VO | 2 (7.0) | Set Theory (reading course) | MLOV | Peter Holy | Tue 4:00pm-5:30pm starts 2011-10-04 | German (English on request) |

250088 | SE | 2 (4.0) | Seminar (Mathematical Logic) | MLOS | Sy-David Friedman | Mon, Wed 2:00pm-3:00pm starts 2011-10-03 | English |

250087 | SE | 2 (4.0) | Research Seminar: Mathematical Logic | MLOS | Sy-David Friedman | Thu 4:00pm-5:30pm starts 2011-10-06 | |

250089 | VO | 2 (4.0) | Selected Topics in Mathematical Logic | MLOV | Sy-David Friedman | Tue, Thu 2:00pm-3:00pm starts 2011-10-04 |

## Subject matters

### Set Theory (reading course)

Time: TUE 4:00pm-5:30pm

starts 2011-10-04

Taking up last semesters course Axiomatic Set Theory 1, we will continue reading in "Kenneth Kunen: Set Theory. An Introduction to Independence Proofs". The first goal of the lecture will be a detailed study of chapter VII (Forcing). For this purpose we will also read parts of chapter II (Infinitary Combinatorics). Furthermore, we will turn towards the study of iterated forcing (probably following "Martin Goldstern: Tools for your Forcing Construction", not following Kunen's book here) and read some selected chapters from the first two parts of "Thomas Jech: Set Theory. The Third Millennium Edition".

In our weekly meetings we shall discuss the read literature, we shall clarify what remained unclear and I will present additional material or material to prepare for next weeks reading. Also we will discuss possible exercises. Furthermore I want to offer the possibility to contact me in case of questions or unclarity on the literature at any time by mail or personally.

If the proposed day and time of the meetings are inconvenient to anybody, they can be relocated - we may discuss this in the first meeting. If you cannot come to the first meeting but still want to take part in this reading course, please contact me by mail.

### Selected Topics in Mathematical Logic

Time: TUE and THU 2:00pm-3:00pm

starts 2011-10-04

This will be a course on Descriptive Complexity Theory, following parts of the book "Finite Model Theory" by Ebbinghaus-Flum. This theory relates logic and complexity theory in the following way: Consider finite structures S. Given a complexity class C, is there a logic L such that the relations on S which belong to C are exactly those which are definable in S using formulas from the logic L? We say that "L captures C". The main theorem of the subject provides a positive answer for the complexity classes LOGSPACE, NLOGSPACE, PTIME, NPTIME and PSPACE, provided one restricts to *ordered* structures. We'll also look at the model theory of the logics that capture these classes and discuss the open question of whether there is a logic that captures PTIME on *arbitrary* finite structures.

### Seminar (Mathematical Logic)

Time: MON and WED 2:00pm-3:00pm

starts 2011-10-03

In this Seminar, students give talks about advanced topics in mathematical Logic. This seminar is intended mainly for students writing their diploma, master or PhD thesis at the KGRC.

### Forschungsseminar aus der Mathematischen Logik

Time: THU 4:00pm-5:30pm

starts 2011-10-06

This is an advanced seminar in mathematical logic for doctoral and postdoctoral researchers.

## Modules

**MLOL** - Mathematische Logik (mathematical logic)

**MLOM** - Axiomatische Mengenlehre (axiomatic set theory)

**MLOS** - Seminare: Mathematische Logik und theoretische Informatik (seminars in mathematical logic and theoretical computer science)

**MLOV** - Vertiefungslehrveranstaltungen für den Studienschwerpunkt
"Mathematische Logik und theoretische Informatik" (courses elaborating on mathematical logic and theoretical computer science as an area of study)