Richard Kaye

contemporaryMathematical Logic

Richard Kaye is a British mathematician and logician at the University of Birmingham, specializing in mathematical logic, models of arithmetic, and computability theory. He is best known for his authoritative textbook on models of Peano arithmetic and for contributions to the study of nonstandard models and the boundaries of primitive recursive computability.

Notable Achievements

Authored 'Models of Peano Arithmetic' (1991), a standard reference in the field

Advanced the study of nonstandard models of first-order Peano arithmetic

Contributed to computability theory, particularly regarding limitations of primitive recursive functions

Proved that the Minesweeper consistency problem is NP-complete

Positions & Arguments(1)

Modality & Possibility

claim

The universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive

Truth & Knowledge

claim

The universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive