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Constructive order types on cuts1

Published online by Cambridge University Press:  12 March 2014

Robert I. Soare
Robert I. Soare*
Affiliation:
University of Illinois at Chicago Circle
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Extract

If A and B are subsets of natural numbers we say that A is recursively equivalent to B (denoted A ≃ B) if there is a one-one partial recursive function which maps A onto B, and that A is recursively isomorphic to B (denoted A ≅ B) if there is a one-one total recursive function which maps A onto B and Ā (the complement of A) onto B#x00AF;.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 2 , 25 July 1969 , pp. 285 - 289
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

This research was supported by National Science Foundation Grant GP 8866.

References

[1] Crossley, J. N., Constructive order types, North-Holland Publishing Co. (to appear).Google Scholar
[2] Dekker, J. C. E. and Myhill, J., Recursive equivalence types, University of California publications in mathematics (N.S.), vol. 3, No. 3 (1960), pp. 67–214.Google Scholar
[3] Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill New York, 1967.Google Scholar
[4] Soare, R. I., Recursion theory and Dedekind cuts, Transactions of the American Mathematical Society (to appear).Google Scholar