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On hyper-torre isols

Published online by Cambridge University Press:  12 March 2014

Rod Downey
Rod Downey*
Affiliation:
Mathematics Department, Victoria University, Wellington, New Zealand
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Extract

As Dekker [3] suggested, certain fragments of the isols can exhibit an arithmetic rather more resembling that of the natural numbers than the general isols do. One such natural fragment is Barback's “tame models” (cf. [2], [6] and [7]), whose roots go back to Nerode [8]. In this paper we study another variety of such fragments: the hyper-torre isols introduced by Ellentuck [4]. Let Y denote an infinite isol with D(Y) the collection of all isols A ≤ f∧(Y) for some recursive and combinational unary function f. (Here, as usual, f ∧ is the Myhill-Nerode extension of f to the isols).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 4 , December 1989 , pp. 1160 - 1166
Copyright
Copyright © Association for Symbolic Logic 1989

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Footnotes

1

The author wishes to thank Joe Barback and Anil Nerode for various discussions and correspondence concerning the theory of isols.

References

REFERENCES

[1] Barback, J., Hyper-torre isols and an arithmetic property. Aspects of effective algebra (Crossley, J. N., editor), Upside Down A Book Company, Steels Creek, 1981, pp. 53–68.Google Scholar
[2] Barback, J., Tame models in the isols, Houston Journal of Mathematics, vol. 12 (1986), pp. 163–175.Google Scholar
[3] Dekker, J. C. E., The minimum of two regressive isols, Mathematische Zeitschrift, vol. 83 (1964), pp. 345–366.CrossRefGoogle Scholar
[4] Ellentuck, E., Hyper-torre isols, this Journal, vol. 46 (1981), pp. 1–5.Google Scholar
[5] McLaughlin, T., Regressive sets and the theory of isols, Marcel Dekker, New York, 1982.Google Scholar
[6] McLaughlin, T., Nerode semirings and Barback's “tame models”, Houston Journal of Mathematics, vol. 12 (1986), pp. 211–223.Google Scholar
[7] McLaughlin, T., Some properties of ∀∃ models in the isols, Proceedings of the American Mathematical Society, vol. 97 (1986), pp. 495–502.Google Scholar
[8] Nerode, A., Diophantine correct nonstandard models in the isols, Annals of Mathematics, ser. 2, vol. 84 (1966), pp. 421–432.CrossRefGoogle Scholar
[9] Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar