# Ackermann's Function Is Not Primitive Recursive

March 23, 2022

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### Abstract

Ackermann's function is defined in the usual way and a number of its elementary properties are proved. Then, the primitive recursive functions are defined inductively: as a predicate on the functions that map lists of numbers to numbers. It is shown that every primitive recursive function is strictly dominated by Ackermann's function. The formalisation follows an earlier one by Nora Szasz.