Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T17:38:05.464Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak presentations of computable fields

Published online by Cambridge University Press:  12 March 2014

Carl G. Jockusch Jr  and
Alexandra Shlapentokh
Carl G. Jockusch Jr
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, E-mail: [email protected]
Alexandra Shlapentokh
Affiliation:
Department of Mathematics, East Carolina University, Greenville, NC 27858, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that for any computable field K and any r.e. degree a there is an r.e. set A of degree a and a field F ≃ K with underlying set A such that the field operations of F (including subtraction and division) are extendible to (total) recursive functions. Further, it is shown that if a and b are r.e. degrees with b ≤ a, there is a 1-1 recursive function f: ℚ → ω such that f(ℚ) ∈ a, f(ℤ) ∈ b, and the images of the field operations of ℚ under f can be extended to recursive functions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 1 , March 1995 , pp. 199 - 208
Copyright
Copyright © Association for Symbolic Logic 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Fried, M. and Jarden, M., Field arithmetic, Springer-Verlag, Berlin, 1986.CrossRefGoogle Scholar
[2]Rabin, M., Computable algebra, general theory, and theory of computable fields, Transactions of the American Mathematical Society, vol. 95 (1960), pp. 341–360.Google Scholar