Universität Wien
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250091 VO Special Topics in Model Theory (2022S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 01.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 03.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 08.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 10.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 15.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 17.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 22.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 24.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 29.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 31.03. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 05.04. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 07.04. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 26.04. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 28.04. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 03.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 05.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 10.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 12.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 17.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 19.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 24.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 31.05. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 02.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 09.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 14.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 21.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 23.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 28.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 30.06. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01

Information

Aims, contents and method of the course

Model theory is a branch of mathematical logic which applies the methods of logic to the study of mathematical structures, and thus has impact on other parts of mathematics (e.g., number theory, analytic geometry).

Since its beginnings in the early decades of the last century, the perception of what the subject is about has gone through various incarnations. A modern view holds that model theory is the "geography of tame mathematics" (Hrushovski), with the goal of identifying those classes of structures whose first-order theories can be understood (in some well-defined technical sense), and exploiting such an understanding as a tool in other parts of mathematics.

This course is a continuation of my class"Model Theory" from last semester. We will further explore this multi-faceted subject, including both its general theory and some applications (mainly to algebra).

Prerequisites: Basic model theory on the level of my class from last semester. Some abstract algebra (groups, rings, fields). If in doubt about your preparation, ask me.

Assessment and permitted materials

Grades will be based on homework sets assigned over the course of the semester.

Minimum requirements and assessment criteria

Examination topics

Omitting types, countable categoricity. Totally transcendental theories, strong minimality, Morley's Theorem. Imaginaries and their elimination. Basic stability theory. Other topics as time permits.

Reading list

I will follow my own notes, but some useful references for this class are:

C. C. Chang and H. J. Keisler, Model Theory, 3rd ed., Studies in Logic and the Foundations of Mathematics, vol. 73. North-Holland Publishing Co., Amsterdam, 1990.

W. Hodges, Model Theory, Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge University Press, Cambridge, 1993.

D. Marker, Model Theory. An Introduction, Graduate Texts in Mathematics, vol. 217. Springer-Verlag, New York, 2002.

K. Tent, M. Ziegler, A Course in Model Theory, Lecture Notes in Logic, vol. 40, Cambridge University Press, Cambridge, 2012.

Association in the course directory

MLOV

Last modified: Fr 22.07.2022 20:28