# Foundations seminar

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

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

## 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).

### Season 2 - Ax-Grothendieck and Model Theory

**21-7-22**(*Will Troiani*): Ax-Grothendieck and model theory (video, transcript)**4-8-22**(*Will Troiani*): The geometric part (video)**18-8-22**(*Will Troiani*): Skolemisation (video)**1-9-22**(*Will Troiani*): Lower-Lowenheim Skolem (video)**15-9-22**(*Will Troiani*): Finishing the Ax-Grothendieck theorem (video)**26-9-22**(*Billy Snikkers*): Filters and Ultrafilters (notes, video, transcript)**3-10-22**(*Billy Snikkers*): Non-standard models of arithmetic (notes, video, transcript)