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A construction for recursive linear orderings

Published online by Cambridge University Press:  12 March 2014

C. J. Ash*
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia

Abstract

We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a linear ordering of type τ, then there is a recursive ordering of type ωβ · τ.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

[1]Ash, C. J., Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees, Transactions of the American Mathematical Society, vol. 298 (1986), pp. 497514.CrossRefGoogle Scholar
[2]Ash, C. J., Labelling systems and r.e. structures, Annals of Pure and Applied Logic, vol. 47 (1990), pp. 99119.CrossRefGoogle Scholar
[3]Ash, C. J. and Knight, J. F., Pairs of recursive structures, Annals of Pure and Applied Logic, vol. 46 (1990), pp. 211234.CrossRefGoogle Scholar
[4]Ash, C. J., Jockusch, C. G., and Knight, J. F., Jumps of orderings, Transactions of the American Mathematical Society, vol. 319 (1990), pp. 573599.CrossRefGoogle Scholar
[5]Love, J., M.Sc. thesis, Monash University, Clayton, Victoria, Australia.Google Scholar
[6]Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar