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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
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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).

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

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Pavlova, (1961), Soviet Math. Dokl. 2, 1017–1019.Google Scholar