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Läuchli's algebraic closure of Q

Published online by Cambridge University Press:  24 October 2008

Wilfrid Hodges
Wilfrid Hodges
Affiliation:
Bedford College, London
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Extract

H. Läuchli (9) constructed, within a model of a weak form of set theory, an algebraic closure L of the field Q of rationals which had no real-closed subfield. Läuchli's construction is easily transferred to a model N of ZF (= Zermelo–Fraenkel set theory without the axiom of Choice), and it follows at once that neither of the two following statements is provable from ZF alone:

Every algebraic closure of Q has a real-closed subfield. (1)

There is, up to isomorphism, at most one algebraic closure of Q. (2)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 2 , March 1976 , pp. 289 - 297
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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