Axiomatizing some small classes of set functions

TL;DR

This paper provides axiomatic characterizations for various classes of set functions, including rudimentary, primitive recursive, safe recursive, and predicatively computable functions, clarifying their foundational properties.

Contribution

It introduces formal axioms that precisely define these classes of set functions, enhancing understanding of their theoretical foundations.

Findings

Axiomatization of rudimentary functions

Axiomatization of primitive recursive functions

Axiomatization of safe recursive and predicatively computable functions

Abstract

In this note we axiomatize the classes of rudimentary functions, primitive recursive functions, safe recursive set functions, and predicatively computable functions.