= Shepherdson's wall
{c}
The obstruction to proving the consistency of nonconstructibility by a uniform <inner model> construction is that, inside a universe satisfying $V=L$, every transitive inner model containing all ordinals has $L$ as its own constructible universe and therefore is the entire ambient universe. The <absoluteness of constructible levels> proves this by induction over successor definability and limit unions. Thus a construction valid in every model of <ZF> cannot always produce such an inner model satisfying $V\ne L$, and in particular cannot always produce one violating <axiom of choice>.
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