A note on computable real fields
Keyword(s):
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 .
2015 ◽
Vol 11
(02)
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pp. 569-592
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2000 ◽
Vol 52
(4)
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pp. 833-848
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1972 ◽
Vol 24
(4)
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pp. 573-579
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2005 ◽
Vol 07
(06)
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pp. 769-786
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