This problem has been debated a lot. The reason for it being a problem is
that there are several versions of the axiom of choice around, some are
constructive, some are not. For some explanations and references you can
have a look at my short note: http://dx.doi.org/10.1002/malq.200410100.
Best regards,
Jesper Carlstrom
Jesse Alama wrote:
> Consider the formulas (in OTTER syntax)
>
> A: all x exist y p(x,y)
> B: all x p(x,f(x)).
>
> Clearly, if B is valid then A is valid. If A is valid, then, by the
> axiom
> of choice, B is valid. Thus the equivalence of the validity of A and B
> depends on a nonconstructive principle, namely the axiom of choice.
> Perhaps this explains why, in the rules for intuitionistic tableaux,
> skolemization is forbidden.
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