Formal systems

• Set theory

• Propositional calculus

• Predicate calculus

• Lambda calculus

  • untyped lambda calculus

  • simply typed lambda calculus

• Combinatory logic

  • SK calculus

  • SKI calculus

  • iota calculus

• Primitive recursive functions

• Formal theories of arithmetic

  • Peano axioms, PA

  • Robinson arithmetic, Q

  • Presburger arithmetic

  • Second-order arithmetic

  • Skolem arithmetic