Eliminating definitions and Skolem functions

Abstract two elements, one can eliminate definitions with a polynomial bound on the increase in proof length. In any classical first-order theory strong enough to code finite functions, including sequential theories, one can also eliminate Skolem functions with a polynomial bound on the increase in proof length.
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    Toshiyasu Arai (1998). Variations on a Theme by Weiermann. Journal of Symbolic Logic 63 (3):897-925.

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