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Partial recursive functions and ω-functions1

Published online by Cambridge University Press:  12 March 2014

C. H. Applebaum  and
J. C. E. Dekker
C. H. Applebaum
Affiliation:
Bowling Green State University, Bowling Green, Ohio
J. C. E. Dekker
Affiliation:
Rutgers University, New Brunswick, New Jersey
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Extract

Let ε stand for the set of all numbers (i.e., nonnegative integers), V for the class of all sets (i.e., subcollections of ε) and for the family of all functions (i.e., mappings from a subset of ε into ε). If ƒ is a function, we write δƒ and ρƒ for its domain and range respectively. The relation of inclusion is denoted by ⊂ and that of proper inclusion by ⊆.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 4 , December 1970 , pp. 559 - 568
Copyright
Copyright © Association for Symbolic Logic 1971

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Footnotes

1

The authors were partially supported by NSF grant GP-8582.

References

[1]Applebaum, C. H., Decompositions and homomorphisms of ω-groups, Doctoral thesis, Rutgers University, 1969.Google Scholar
[2]Dekker, J. C. E., Infinite series of isols, Proceedings of Symposia in Pure Mathematics, vol. 5 (1962), pp. 77–96.CrossRefGoogle Scholar
[3]Dekker, J. C. E., Good choice sets, Annali della Scuola Normale Superiore di Pisa, Serie III, vol. 20 (1966), pp. 367–393.Google Scholar
[4]Dekker, J. C. E. and Myhill, J., Recursive equivalence types, University of California Publications in Mathematics (N.S.), vol. 3 (1960), pp. 67–213.Google Scholar
[5]Gonshor, H., The category of recursive functions, Notices of the American Mathematical Society, vol. 15 (1968), p. 473.Google Scholar