Universität Wien

250138 VO Model Theory (2024W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle
Tu 22.10. 13:15-14:45 Seminarraum 10, Kolingasse 14-16, OG01

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Note that the first lecture of this class will be on **Thursday, October 10th**.

  • Thursday 10.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 15.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 17.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 24.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 29.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 31.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 05.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 07.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 12.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 14.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 19.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 21.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 26.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 28.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 03.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 05.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 10.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 12.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 17.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 07.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 09.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 14.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 16.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 21.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 23.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 28.01. 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 will serve as a first introduction to this multi-faceted subject. Both the development of general theory and some applications (mainly to algebra) will be presented.

Assessment and permitted materials

Final exam on Thursday, January 30, 2025, 1:15-2:45 pm.

Minimum requirements and assessment criteria

Examination topics

Review of structures, theories, ultraproducts, proof of the Compactness Theorem, and first applications of Compactness. Boolean algebras, types, saturation. Model completeness, quantifier elimination, and applications to algebraically closed and real closed fields. 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: Th 10.10.2024 10:26