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Countable vector spaces with recursive operations Part I1

Published online by Cambridge University Press:  12 March 2014

J. C. E. Dekker
J. C. E. Dekker*
Affiliation:
RutgersThe State University and Institute for Advanced Study
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Extract

We use the word “number” for “nonnegative integer” and “set” for collection of numbers. The set of all numbers is denoted by ε and the empty set by ο. We write ⊂ for the relation of inclusion and ⊆ for that of proper inclusion. If ƒ is a function from a subset of ε into ε, its domain and range are denoted by δƒ and ρƒ respectively. For any collection Γ of entities, card Γ or card (Γ) stands for the cardinality of Γ. The cardinality of the continuum is denoted by c.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 363 - 387
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

This paper was written while the author was supported by a grant from the Rutgers Research Council. Some of the results were presented at the Boston meeting of the ASL, December 28, 1967. See the abstract [3].

References

[1]Dekker, J. C. E. and Myhill, J., Recursive equivalence types, University of California Publications in Mathematics (N.S.), vol. 3 (1960), pp. 67–214.Google Scholar
[2]Dekker, J. C. E., Les fonctions combinatoires et les isols, Gauthier-Villars, Paris, 1966.Google Scholar
[3]Dekker, J. C. E., On certain vector spaces of isolic dimension, Part I, abstract, this Journal, vol. 33 (1968), p. 642.Google Scholar
[4]Hassett, M. J., Recursive equivalence types and groups, this Journal, vol. 34 (1969), pp. 13–20.Google Scholar
[5]Raikov, D. A., Vector spaces, P. Noordhoff Ltd., Groningen, 1965.Google Scholar
[6]Rice, H. G., Classes of recursively enumerable sets and their decision problems, Transactions of the American Mathematical Society, vol. 74 (1953), pp. 358–366.CrossRefGoogle Scholar