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)