Universität Wien
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250138 VO Model Theory (2024W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle
Di 21.01. 13:15-14:45 Seminarraum 10, Kolingasse 14-16, OG01

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

  • Donnerstag 10.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 15.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 17.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 22.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 24.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 29.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 31.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 05.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 07.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 12.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 14.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 19.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 21.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 26.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 28.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 03.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 05.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 10.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 12.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 17.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 07.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 09.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 14.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 16.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 23.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 28.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 30.01. 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

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

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

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.

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: Fr 27.12.2024 16:26