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Bases and α-dimensions of countable vector spaces with recursive operations 1

Published online by Cambridge University Press:  12 March 2014

Alan G. Hamilton
Alan G. Hamilton*
Affiliation:
University of Stirling
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Extract

This paper is based on the notions originally described by Dekker [2], [3], and the reader is referred to these for explanation of notation etc. Briefly, we are concerned with a countably infinite dimensional countable vector space Ū with recursive operations, regarded as being coded as a set of natural numbers. Necessarily, then, Ū must be a vector space over a field which itself is in some sense recursively enumerable and has recursive operations.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 1 , March 1970 , pp. 85 - 96
Copyright
Copyright © Association for Symbolic Logic 1970

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Footnotes

1

The contents of this paper form part of a thesis written under the supervision of J. N. Crossley and submitted to the University of Oxford for the degree of Doctor of Philosophy.

References

[1] Crossley, J. N., Constructive order types, North-Holland, Amsterdam, 1969.Google Scholar
[2] Dekker, J. C. E., On certain vector spaces of isolic dimension. Part 1, this Journal, vol. 33 (1968), p. 642.Google Scholar
[3] Dekker, J. C. E., Countable vector spaces with recursive operations. Part 1, this Journal, vol. 34 (1969), 363–387.Google Scholar
[4] Hamilton, A. G., Mathematical structures and recursive equivalence, Thesis, Oxford, 1969.Google Scholar