Universität Wien

250119 VO Model theory (2021W)

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

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Freitag 01.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 06.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 08.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 13.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 15.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 20.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 22.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 27.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 29.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 03.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 05.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 10.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 12.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 17.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 19.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 24.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 26.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 01.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 03.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 10.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 15.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 17.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 07.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 12.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 14.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 19.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 21.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Mittwoch 26.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Freitag 28.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

Review of structures, theories, ultraproducts, proof of the Compactness Theorem. Quantifier elimination, model completeness. Types, saturation, omitting types. Totally transcendental theories, strong minimality, Morley's Theorem. Other topics as time permits.

Literatur

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.

Zuordnung im Vorlesungsverzeichnis

MLOV

Letzte Änderung: Mo 28.02.2022 10:30