In a given model of ZF either choice is true or it is false. In the absence of the Axiom of Choice you can’t say that not all fields have algebraic closures. W

In a given model of ZF either choice is true or it is false. In the absence of the Axiom of Choice you can’t say that not all fields have algebraic closures. What you can say is that there is a model in which there are fields with no algebraic closure.