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I hope this is not too trivial, but I think this may be well known to someone (not me).

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    $\begingroup$ Just the classical form? $\endgroup$
    – François G. Dorais
    Oct 11, 2013 at 15:53
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    $\begingroup$ What do you mean by "reverse math"? $\endgroup$
    – Liviu Nicolaescu
    Oct 11, 2013 at 16:34
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    $\begingroup$ en.wikipedia.org/wiki/Reverse_mathematics $\endgroup$
    – Benjamin Steinberg
    Oct 11, 2013 at 17:09
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    $\begingroup$ At least over an algebraically closed field, any given instance will be provable in that complete theory. On the other hand, the usual assertion which quantifies over all line bundles is indirectly making some statement in the language of arithmetic, much as here: mathoverflow.net/questions/105478/… A priori, the same questions apply. $\endgroup$
    – Adam Epstein
    Oct 11, 2013 at 18:34

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