Hostname: page-component-76c49bb84f-ndtt8 Total loading time: 0 Render date: 2025-07-05T14:53:01.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive density types and Nerode extensions of arithmetic

Published online by Cambridge University Press:  09 April 2009

P. Aczel
P. Aczel
Affiliation:
Department of Mathematics Manchester University, England
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.

The notion of a recursive density type (R.D.T.) was introduced by Medvedev and developed by Pavlova (1961). More recently the algebra of R.D.T.'s was initiated by Gonshor and Rice (1969). The R.D.T.'s are equivalence classes of sets of integers, similar in many respects to the R.E.T.'s. They may both be thought of as effective analogues of the cardinal numbers. While the equivalence relationfor R.E.T.'s is defined in terms of partial recursive functions, that for R.D.T.'s may be characterized in terms of recursively bounded partial functions (see 4.22a).

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 2 , September 1975 , pp. 146 - 158
Copyright
Copyright © Australian Mathematical Society 1975

References

Ellentuck, E. (1967), ‘Universal isols’, Math. Z. 98, 1–8.CrossRefGoogle Scholar
Gonshor, H. and Rice, H. (1969), ‘Recursive density types’, Trans. Amer. Math. Soc. 140, 493–503.CrossRefGoogle Scholar
Nerode, A. (1961), ‘Extensions to isols’, Ann. of Math. 73, 362–403.CrossRefGoogle Scholar
Pavlova, (1961), Soviet Math. Dokl. 2, 1017–1019.Google Scholar