Submission date: 14 November 2008.

Abstract:

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.

Mathematics Subject Classification: 03C60

Keywords and phrases:

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