# Ackermann's Function Is Not Primitive Recursive

 Title: Ackermann's Function Is Not Primitive Recursive Author: Lawrence C. Paulson Submission date: 2022-03-23 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. BibTeX: @article{Ackermanns_not_PR-AFP, author = {Lawrence C. Paulson}, title = {Ackermann's Function Is Not Primitive Recursive}, journal = {Archive of Formal Proofs}, month = mar, year = 2022, note = {\url{https://isa-afp.org/entries/Ackermanns_not_PR.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.