Infinitary logic (Winter 2025, TU Wien)

Time: Fridays 1pm–3pm (new time).
Place: Seminar room on the 5th floor in the green area of the Freihaus building of TU Wien.

October 10th, 2025. Introduction. Recap (first-order logic: compactness, completeness, the Löwenheim-Skolem theorem; ultrafilters; ordinals and cardinals). Abstract definition of a logic. Some examples of logics. The downward Löwenheim-Skolem theorem for L_{\omega_1,\omega}.
October 17th, 2025. More examples of logics. Consistency properties. The Model Existence Theorem for L_{\omega_1,\omega}.
October 24th, 2025. Proof of the The Model Existence Theorem. Hanf numbers.
October 31st, 2025. Lower bound for the Hanf number of L_{\omega_1,\omega}. Ramsey's Theorem. The Erdős-Rado Theorem.
November 14th, 2025.
November 21st, 2025.
November 28th, 2025.
December 5th, 2025.
December 12th, 2025.
January 9th, 2025.
January 16th, 2025.
January 23rd, 2025.

[1] J. L. Bell. Infinitary Logic. In: Stanford Encyclopedia of Philosophy (2023). Available at https://plato.stanford.edu/entries/logic-infinitary/

[2] T. Jech. Set Theory: The Third Millenium Edition (2023). Springer.

[3] C. C. Chang and H. J. Keisler. Model Theory (1990). North-Holland.

[4]. D. Marker. Lectures on Infinitary Model Theory (2013). Cambridge University Press.

More to be announced.