Läuchli's algebraic closure of Q
Wilfrid Hodges · Mathematical Proceedings of the Cambridge Philosophical Society · 1976
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)