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Isomorphisms on countable vector spaces with recursive operations

Published online by Cambridge University Press:  09 April 2009

Robert I. Soare
Robert I. Soare
Affiliation:
University of Illinois at Chicago Circle Chicago, Illinois, 60680, U. S. A.
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Terminology and notation may be found in Dekker [1] and [2]. Briefly, we fix a recursively enumerable (r.e.) field F with recursive structure, and let Ū be the vector space over F consisting of ultimately vanishing countable sequences of elements of F with the usual definitions of vector addition and multiplication by a scalar. A subspace V of Ū is called an α-space if V has a basis B which is contained in some r.e. linearly independent set S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 2 , September 1974 , pp. 230 - 235
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Dekker, J. C. E., ‘Countable vector spaces with recursive operations’, Journal of Symbolic Logic 34 (1969), 363–387.CrossRefGoogle Scholar
[2]Dekker, J. C. E., ‘Countable vector spaces with recursive operations’, Journal of Symbolic Logic 36 (1971), 477–493.CrossRefGoogle Scholar
[3]Dekker, J. C. E. and Myhill, J., ‘Recursive equivalence types’, University of California publications in mathematics (N. S.) (1960), 67–214.Google Scholar
[4]Hamilton, A. G., ‘Bases and a-dimensions of countable vector spaces with recursive operations’, Journal of Symbolic Logic 35 (1970), 65–96.CrossRefGoogle Scholar
[5]Rogers, H. Jr, Theory of Recursive Functions and Effective Computability, (McGraw-Hill, New York, 1967).Google Scholar
[6]Soare, R. I., ‘Constructive order types on cuts’, Journal of Symbolic Logic 34 (1969), 285–289.CrossRefGoogle Scholar