# Foundations seminar

A seminar on the nature of mathematical objects, logic, Gödel’s theorems.

**Co-organisers**: Billy Snikkers and Will Troiani.**Venue**: Moonlight Forest.

## Schedule

There is a timezone change on the 2nd October for daylight savings in Melbourne. The foundations seminar timeslot will stick to Melbourne time, which will change from AEST (UTC +10) to AEDT (UTC +11).

The next few seminars will be as follows:

**26-9-22 21:00 AEST (UTC +10)**(*Billy Snikkers*): Ultrafilters (notes)**3-10-22 21:00 AEDT (UTC +11)**(*Billy Snikkers*): Non-standard models of arithmetic**17-10-22 21:00 AEDT (UTC +11)**(TBA): TBA

From 17-10-22, foundations will run every 2 weeks at 21:00 AEDT (UTC +11), immediately after the Shadows of Computation lecture.

## Past seminars

### Season 1 - First Order Logic, Soundness, Completeness, Incompleteness

- Seminar 1A: variables, terms, relation symbols, function symbols, formulas and free variables.
- Seminar 1B: first order languages, interpretations and theories.
- Seminar 2: natural deduction as a proof system I.
- Seminar 3: natural deduction as a proof system II, soundness.
- Seminar 6: discharging hypotheses and Curry-Howard.
- Seminar 7: any consistent, complete and saturated system is satisfiable.
- Seminar 8: Completeness theorem.
- Seminar 9: Gödel’s theorem I
- Seminar 10: Gödel’s theorem II
**10-2-22**(*Will Troiani*): Gödel’s incompleteness theorem Part 3 (video).**17-2-22**(*Will Troiani*): Gödel’s incompleteness theorem Part 4 (video).**3-3-22**(*Will Troiani*): Gödel’s incompleteness theorem Part 5 (video).**17-3-22**(*Will Troiani*): Gödel’s incompleteness theorem Part 6 (video).