A note on computable real fields
The work
| Authors | E. W. Madison |
|---|---|
| Editors | |
| Type | article |
| Year | 1970 |
| Citekey | madison1970note |
Where it appeared
| Published in | Journal of Symbolic Logic |
|---|---|
| Publisher | Cambridge University Press |
| Volume | 35 |
| Issue | 2 |
| Pages | 239--241 |
Identifiers
| DOI | 10.2307/2270515 |
|---|---|
| OpenAlex | W2171488860 |
Access
| Landing page | https://doi.org/10.2307/2270515 |
|---|
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Abstract
It is well known that every field (formally, real field ) has an algebraic closure (real-closure ). This is to say is an algebraic extension of which is algebraically closed (real-closed). Of course, certain properties of carry over to . In particular, M. O. Rabin has proved in [3] that the algebraic closure—which is of course unique up to isomorphism—of a computable field is computable. The purpose of this note is to establish an analogue of Rabin's theorem for formally real fields. It is clear that a direct analogue can be formulated only in the case of ordered fields, for otherwise there may be many (nonisomorphic) such .
How it got here
| How it got here | agent via openalex |
|---|---|
| Added | 2026-10-24 09:04 UTC |
| Not denied by | a person 2026-10-29 17:12 UTC |
Filed under
Cite it as
@article{madison1970note,
title = {A note on computable real fields},
author = {E. W. Madison},
year = {1970},
journal = {Journal of Symbolic Logic},
publisher = {Cambridge University Press},
volume = {35},
number = {2},
pages = {239--241},
doi = {10.2307/2270515},
}
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