Computability Theory

Introduction to Computability Theory

These are notes for a short introductory course on Computability Theory (or recursive function theory). The basic notion of computability is defined in terms of a simple imperative programming language.

Lattice Representations for Computability Theory

Computability Theory

Enumeration Reducibility and Computable Structure Theory

In classical computability theory the main underlying structure is that of the natural numbers or equivalently a structure consisting of some constructive objects, such as words in a finite alphabet. In the 1960’s computability theorists saw it as a challenge to extend the notion of computable to arbitrary structure. The resulting subfield of computability theory is commonly referred to as comp...

Computing with functionals - computability theory or computer science?

We review some of the history of the computability theory of functionals of higher types, and we will demonstrate how contributions from logic and theoretical computer science have shaped this still active subject.