Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-04T21:21:12.130Z Has data issue: false hasContentIssue false
  • English
  • Français

On the set of finite subsets of a set

Published online by Cambridge University Press:  09 April 2009

J. L Hickman
J. L Hickman
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra.
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.

We sometimes think of medial (that is, infinite Dedekind-finite) sets as being “small” infinite sets. Medial cardinals can be defined as those cardinals that are incomparable to ℵℴ; hence we tend to think of them as being spread out on a plane “just above” the natural numbers, which seems to lend support to the view expressed above that medial sets are “small”.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 1 , August 1975 , pp. 38 - 45
Copyright
Copyright © Australian Mathematical Society 1975

References

Jech, T. (1971), Lectures in Set Theory. (Springer-Verlag 1971.)Google Scholar
Monro, G. P. (1973), ‘Small sets with large powersets’, Bull. Austral. Math. Soc. 8, 413–422.CrossRefGoogle Scholar
Rosser, J. Barkley (1969), ‘Simplified Independence Proofs’. (Academic Press 1969).Google Scholar
Tarski, A. (1949), ‘Cancellation laws in the arithmetic of cardinals’, Fund Math. 36, 77–92.CrossRefGoogle Scholar
Truss, J. K. (to appear), ‘The well-ordered and well-orderable subsets of a set’, Zeit. f. math. Logik.Google Scholar