Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T22:57:14.179Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on principal sequences

Published online by Cambridge University Press:  18 May 2009

B. Rotman
B. Rotman
Affiliation:
Sir John Cass College, London
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A fundamental problem in the theory of ordinals is the assignation of principal sequences to limit numbers of the second number class.

It is our main object here to show that a certain class of methods, which are a natural generalisation of those used in the solution of the corresponding problem for the real numbers (the description of which we omit), must fail to solve the problem. The methods are those which rest on the following assumption: the principal sequence assigned to any limit number of the second number class is determined once the first i terms of that sequence are known.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 3 , January 1964 , pp. 133 - 135
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

1.Bachmann, H., Transfinite Zahlen (Ergeb. der Math. u. ihrer Grenzgeb., Berlin, 1955).CrossRefGoogle Scholar
2.Bloch, G., Sur les ensembles stationnaires de nombres ordinaux et les suites distinguées de fonctions regressives, C. R. Acad. Sc. Paris 236 (1952), 265–268.Google Scholar
3.Denjoy, A., L'Énumération Transfinie, Livre 2: L'arithmétisation du transfini, deuxième partie—Les suites canoniques (Paris, 1952), 439–607.Google Scholar