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On hyper-torre isols

  • Rod Downey (a1)


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 Af(Y) for some recursive and combinational unary function f. (Here, as usual, f is the Myhill-Nerode extension of f to the isols).



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[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. 5368.
[2]Barback, J., Tame models in the isols, Houston Journal of Mathematics, vol. 12 (1986), pp. 163175.
[3]Dekker, J. C. E., The minimum of two regressive isols, Mathematische Zeitschrift, vol. 83 (1964), pp. 345366.
[4]Ellentuck, E., Hyper-torre isols, this Journal, vol. 46 (1981), pp. 15.
[5]McLaughlin, T., Regressive sets and the theory of isols, Marcel Dekker, New York, 1982.
[6]McLaughlin, T., Nerode semirings and Barback's “tame models”, Houston Journal of Mathematics, vol. 12 (1986), pp. 211223.
[7]McLaughlin, T., Some properties of ∀∃ models in the isols, Proceedings of the American Mathematical Society, vol. 97 (1986), pp. 495502.
[8]Nerode, A., Diophantine correct nonstandard models in the isols, Annals of Mathematics, ser. 2, vol. 84 (1966), pp. 421432.
[9]Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.

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On hyper-torre isols

  • Rod Downey (a1)


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