Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-04T18:42:50.657Z Has data issue: false hasContentIssue false
  • English
  • Français

Transfinite ordinals in recursive number theory

Published online by Cambridge University Press:  12 March 2014

R. L. Goodstein
R. L. Goodstein*
Affiliation:
The University, Reading, England
Get access Rights & Permissions [Opens in a new window]

Extract

The possibility of constructing a numerical equivalent of a system of trans-finite ordinals, in recursive number theory, was briefly indicated in a previous paper, where consideration was confined to ordinals less than ε (the first to satisfy ε = ω). In the present paper we construct a representation, by functions of number-theoretic variables, for ordinals of any type.

In addition to definite numerals, and numeral variables, we introduce majorant variables σ, ω, ωr , r ≧ 1. A relation containing a single majorant variable σ is required to hold, not necessarily for all non-negative integral values of σ, but for all values greater than some assigned constant.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 12 , Issue 4 , December 1947 , pp. 123 - 129
Copyright
Copyright © Association for Symbolic Logic 1947

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 In this Journal, vol. 9(1944), pp. 33–41.

2 Cf. Ackermann, W., Zum Hibertschen Aufbau der reelen Zahlen, Mathematische Annalen, vol. 99(1928), p. 120.CrossRefGoogle Scholar