Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-684bc48f8b-9ddkh Total loading time: 0.246 Render date: 2021-04-12T13:50:38.603Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
The Journal of Symbolic Logic The Journal of Symbolic Logic

Article contents

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: jockusch@math.uiuc.edu
Alexandra Shlapentokh
Affiliation:
Department of Mathematics, East Carolina University, Greenville, NC 27858, E-mail: mashlape@ecuvax.cis.ecu.edu
Corresponding
E-mail address:
jockusch@math.uiuc.edu
mashlape@ecuvax.cis.ecu.edu
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.
If you should have access and can't see this content please contact technical support.

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

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 3 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 12th April 2021. This data will be updated every 24 hours.

4
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Weak presentations of computable fields
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Weak presentations of computable fields
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Weak presentations of computable fields
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *