Exponential algebraicity in exponential fields
classification
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exponentialalgebraicschanuelalgebraicityalwaysclosureconjecturecorollary
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I give an algebraic proof that the exponential algebraic closure operator in an exponential field is always a pregeometry, and show that its dimension function satisfies a weak Schanuel property. A corollary is that there are at most countably many essential counterexamples to Schanuel's conjecture.
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