Universität Wien

250104 VO Advanced topics in mathematical logic (2019S)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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.

Mindestanforderungen und Beurteilungsmaßstab

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.

Prüfungsstoff

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

Literatur

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

Zuordnung im Vorlesungsverzeichnis

MLOV

Letzte Änderung: Fr 18.11.2022 00:23