Some possible topics for projects:
  1. Linear logic or other substructural logics (possible sources: Proofs and Types by Girard, Basic Proof Theory by Troelstra and Schwichtenberg, An Introduction to Substructural Logics by Greg Restall)
  2. The Curry-Howard Isomorphism (possible sources: Proofs and Types by Girard, Basic Proof Theory by Troelstra and Schwichtenberg)
  3. Model Theory of non-classical logic (possible sources: A Short Introduction to Intuitionistic Logic by Mints)
  4. Reverse Mathematics (possible sources: Subsystems of Second Order Arithmetic by Stephen Simpson)
  5. An alternate approach to ordinal analysis, such as ε-substitution (see Gentzen-type systems and Hilbert's epsilon substitution method by Mints) or model-theoretically (see A model-theoretic approach to ordinal analysis by Avigad and Sommer)
  6. Cut-elimination for an appropriate modal or other logic (possible sources: many papers of this type have been published)
  7. Foundational concerns (possible sources: In the Light of Logic, by Solomon Feferman)