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Boolean combinations of r.e. open sets

Published online by Cambridge University Press:  12 March 2014

Louise Hay
Louise Hay*
Affiliation:
University of Illinois at Chicago Circle, Chicago, Illinois 60680
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Extract

In [2], [3], J. Grassin characterized those classes of sets which are expressible as a Boolean combination of open sets in the Baire topology on the power set of the natural numbers. From this characterization he deduced that if is a Boolean combination of recursive open sets, then the minimum length for any Boolean combination representing can be realized using recursive open sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 1 , March 1976 , pp. 235 - 238
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] Ershov, Y. L., A hierarchy of sets. I, Algebra and Logic, vol. 7 (1968), pp. 25–43.CrossRefGoogle Scholar
[2] Grassin, J., Ensembles d'indices des combinaisons booléennes d'ouverts dont une clé est recursivement énumérable, Thesis, Université d'Orléans, 1972.Google Scholar
[3] Grassin, J., Index sets in Ershov's hierarchy, this Journal, vol. 39 (1974), pp. 97–104.Google Scholar
[4] Kuratowski, K., Topology, vol. I, Academic Press, New York, 1966.Google Scholar
[5] Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar