Type theory

The topic of type theory is fundamental both in logic and computer science. We limit ourselves here to sketch some aspects that are important in logic. For the importance of types in computer science, for instance:

1. Reynolds 1983 and 1985.
2. Paradoxes and Russell's Type Theories
3. Simple Type Theory and the λ -Calculus.

Church's type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory.