We prove an effective form of Wilkie's conjecture in the structure generated by restricted sub-Pfaffian functions: the number of rational points of height H lying in the transcendental part of such a set grows no faster than some power of log\, H. Our bounds depend only on the Pfaffian complexity of the sets involved. As a corollary we deduce Wilkie's original conjecture for Rₑₓₚ in full generality.
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Binyamini et al. (2024) studied this question.
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