Skip to main content Accessibility help
×
Home

On hyper-torre isols

  • Rod Downey (a1)

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

Copyright

References

Hide All
[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.

Related content

Powered by UNSILO

On hyper-torre isols

  • Rod Downey (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.