Universität Wien

250104 VO Advanced topics in mathematical logic (2019S)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Tuesday 05.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 06.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 13.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 19.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 20.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 26.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 27.03. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 02.04. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 03.04. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 09.04. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 10.04. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 30.04. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 07.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 08.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 14.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 15.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 21.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 22.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 28.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Wednesday 29.05. 13:00 - 14:00 (ehem.Seminarraum d. Inst. f. Formale Logik, Währinger Straße 25, 2. Stock, Raum 101)
Tuesday 04.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 05.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 18.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 25.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.06. 13:15 - 14:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

What original ideas lead to the breakthrough results of infinite combinatorics in the last 30 years? Which methods found the widest range of applications? The main purpose of this course is to overview novel techniques from the theory of (mostly) discrete structures of small uncountable size. We will survey applications from graph theory, the geometry of Euclidean spaces, topology, analysis and algebra. We will cover inductive constructions based on elementary submodels; coherent maps, walks on ordinals and applications of rho-functions; and various approximation schemes. We shall also point out several open problems that wait to be solved. The course aims to provide a working mathematician's toolbox without going too deep into any one specific area.
The course is aimed at advanced bachelor and graduate students with an interest in combinatorial questions, set theory or logic.

Assessment and permitted materials

The final mark is composed of three components: participation (50%), submitted assignments (30%) and a 'presentation in pairs' component (20%).

Participation (50%): you are expected to attend the lectures and encouraged to actively participate in class discussion.

Assignments (30%): at each lecture, a number of exercises and problems will be announced (approx. 5 per lecture). You select the questions you like and submit solutions typed in Latex; the problems announced at a given lecture can be submitted for 2 weeks. Each correct solution for the exercises amounts to 0.5%, each problem to 1% of the maximal 30% that can be earned.

Presentation in pairs (20%): working in pairs, you will select a recent result/article closely related to the main topics of the course (plenty of recommendations will be provided). After understanding the material, you prepare a joint 30-minute presentation on the result. You should outline the context, main ideas and connections to the course material. Presentations will take place during the examination period.

Minimum requirements and assessment criteria

There are no official prerequisites; however, we will assume familiarity with basic concepts of set theory e.g., ordinals and cardinals; stationary and club sets; transfinite induction; what is a formula, satisfaction and a model of a theory; basic concepts in graph theory and Ramsey's theorem on the natural numbers. See Chapter I and II of [Kunen, Kenneth. Set theory an introduction to independence proofs. Vol. 102. Elsevier, 2014].

The official passing grade will be 50% which can be earned with any combination of the above assessment components.

Examination topics

The 'Presentation in pairs' component will be counted as the final examination. Please see above for details.

Reading list

Assignments, course information and all related course materials will be posted on Moodle. In addition to office hours, you will have the chance to ask questions and discuss the topics on the Moodle forum.

Please find the detailed syllabus here: http://www.logic.univie.ac.at/~soukupd73/teach.xhtml

Association in the course directory

MLOV

Last modified: Fr 18.11.2022 00:23