Introduction to mathematical logic (SoSe 2019)


The lecture takes place on Thursdays from 12:15 to 1:45pm and on Fridays from 9:30 to 11am in the lecture room of the Kurt Gödel Research Center (Währinger Straße 25, 2nd floor, 02.101, floor plan).

Details about the contents of each lecture can be found here.
Additional handwritten notes: How to obtain maximal filters using HMP.
Ultraproducts and the Compactness Theorem. DLO is not kappa categorical for uncountable cardinals kappa.

To pass this class you need to take an oral exam. Possible dates for the exam are June 25th, July 10th, and October 3rd. More dates will be offered on request during the winter semester.

Monroe Eskew will offer a Proseminar (Exercise session) for this lecture. I strongly recommend to also participate in the Proseminar.

Contents

This lecture will be an introduction to different areas of mathematical logic and their connections. We start with a review of formulas and structures and introduce the method of ultrapower construction. This will lead us to a closer look into the area of model theory which we will augment with the study of types and the structure of countable models. Moreover, we will study classical games which are used in model theory and are related to set theory. Afterwards we will prove Gödel's first incompleteness theorem in full generality.

This lecture will be self-contained. Nevertheless some familiarity with the contents of the lecture "Grundzüge der mathematischen Logik" (e.g. see WiSe 2018/19) might be helpful.

References

  1. Tent, K., & Ziegler, M. (2012). A Course in Model Theory. Cambridge University Press.
  2. Goldstern, M., & Judah, H. (1998). The Incompleteness Phenomenon. Taylor & Francis.
  3. Väänänen, J. (2011). Models and Games. Cambridge University Press.
  4. Boolos, G. S., Burgess, J. P., & Jeffrey, R. C. (2007). Computability and Logic. Cambridge University Press.
  5. Müller, M. Skript zur Unvollständigkeit.
  6. Gitman, V. Course notes: Logic I.