Chapter XIX: Between number theory and set theory

  • 1

    Readers

    Mendeley users who have this article in their library.
  • 0

    Citations

    Citations of this article.

Abstract

This chapter discusses a number of interconnections between number theory, that is, the theory of natural numbers or nonnegative integers and certain systems of set theory. Set theory is equivalent to number theory. If infinite sets are allowed but not impredicative sets, then set theory still resembles number theory quite well. The big gap between number theory and set theory proper is the introduction of impredicative sets in set theory. The chapter formulates these connections between number theory and set theory. The chapter reviews the general set theory or Zermelo's set theory minus the axiom of infinity. The system G is the basic system of general set theory including the axiom of extensionality, the Aussonderungs axiom, and an axiom assuring the existence of finite sets. The system Z is the ordinary system of elementary number theory. © 1963, Science Press

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

There are no authors.

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free