Skip to main content Accessibility help
×
Home

Models of arithmetic and subuniform bounds for the arithmetic sets

  • Alistair H. Lachlan (a1) and Robert I. Soare (a2)

Abstract

It has been known for more than thirty years that the degree of a non-standard model of true arithmetic is a subuniform upper bound for the arithmetic sets (suub). Here a notion of generic enumeration is presented with the property that the degree of such an enumeration is an suub but not the degree of a non-standard model of true arithmetic. This answers a question posed in the literature.

Copyright

References

Hide All
[1]Friedberg, R. M., A criterion for completeness of degrees of unsolvability, this Journal, vol. 22 (1957), pp. 159160.
[2]Knight, J., Lachlan, A. H., and Soare, R. I., Two theorems on degrees of models of arithmetic, this Journal, vol. 49 (1984), pp. 425436.
[3]Knight, J. F., Additive structure in uncountable models for a fixed completion of p, this Journal, vol. 55 (1983), pp. 623628.
[4]Knight, J. F., Degrees of models with prescribed Scott set, Proceedings of the U.S.-Israel workshop on model theory in mathematical logic: Classification theory, Chicago, December 15–19, 1985 (Baldwin, John, editor), Lecture Notes in Mathematics, no. 1292, Springer-Verlag, Berlin, Heidelberg, New York, 1987, pp. 182191.
[5]Knight, J. F., A metatheorem for constructions by finitely many workers, this Journal, vol. 55 (1990), pp. 787804.
[6]Lachlan, A. H. and Soare, R. I., Models of arithmetic and upper bounds for arithmetic sets, this Journal, vol. 59 (1994), pp. 977983.
[7]Lerman, M., Upper bounds for the arithmetical degrees, Annals of Pure and Applied Logic, vol. 29 (1985), pp. 225253.
[8]Macintyre, A. and Marker, D., Degrees of recursively saturated models, Transactions of the American Mathematical Society, vol. 282 (1984), pp. 539554.
[9]Marker, D., Degrees of models of true arithmetic, Proceedings of the Herbrand symposium: Logic colloquium (Stern, J., editor), North-Holland, Amsterdam, 1981, pp. 233242.
[10]Scott, D., Algebras of sets binumerable in complete extensions of arithmetic, Recursive function theory: Proceedings ofsympos. in pure mathematics, vol. 5, American Mathematical Society, Providence, 1961, pp. 117121.
[11]Solovay, R. M., Degrees of models of true arithmetic, preliminary version, unpublished manuscript, 1984.

Related content

Powered by UNSILO

Models of arithmetic and subuniform bounds for the arithmetic sets

  • Alistair H. Lachlan (a1) and Robert I. Soare (a2)

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.