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Countable vector spaces with recursive operations Part II1

Published online by Cambridge University Press:  12 March 2014

J. C. E. Dekker
J. C. E. Dekker*
Affiliation:
Rutgers University, New Brunswick, New Jersey 08903
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Extract

We use the same terminology and notations as in Part I of this paper [3], but numerals in square brackets refer to the references at the end of the present part. The word “space” will be used in the sense of “subspace of ŪF”. A. G. Hamilton [6] proved that any two α-bases of any α-space are recursively equivalent (see also [5]). This means that dimαV, introduced in [3] only for an isolic α-space V, can be defined for anyα-space V. Several results of [3] can therefore be strengthened. These and some other improvements are listed in §8. It is proved in §9 that every α-subspace of an isolic α-space is again an isolic α-space.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 3 , September 1971 , pp. 477 - 493
Copyright
Copyright © Association for Symbolic Logic 1972

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Footnotes

1

Research supported by the Rutgers Research Council and NSF grant GP-11509. Some of the results were announced in the abstract [4].

References

[1]Applebaum, C. H. and Dekker, J. C. E., Partial recursive functions and ω-functions, this Journal, vol. 35 (1970), pp. 559–568.Google Scholar
[2]Dekker, J. C. E., Good choice sets, Annali della Scuola Normale Superiore di Pisa, Serie III, vol 20 (1966), pp. 367–393.Google Scholar
[3]Dekker, J. C. E., Countable vector spaces with recursive operations. Part I, this Journal, vol. 34 (1969), pp. 363–387.Google Scholar
[4]Dekker, J. C. E., On α-homomorphisms between α-spaces, abstract, this Journal, vol. 35 (1970), p. 184.Google Scholar
[5]Dekker, J. C. E., Two notes on vector spaces with recursive operations, Notre Dame Journal of Formal Logic vol. 12 (1971), pp. 329–334.CrossRefGoogle Scholar
[6]Hamilton, A. G., Bases and α-dimensions of countable vector spaces with recursive operations, this Journal, vol. 35 (1970), pp. 85–96.Google Scholar