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Note on generalizing theorems in algebraically closed fields

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Source

Archive for Mathematical Logic 37 (1998) 297–307
(with Matthias Baaz)

Abstract

The generalization properties of algebraically closed fields ACF_p of characteristic p > 0 and ACF₀ of characteristic 0 are investigated in the sequent calculus with blocks of quantifiers. It is shown that ACF_p admits finite term bases, and ACF₀ admits term bases with primality constraints. From these results the analogs of Kreisel's Conjecture for these theories follow: If for some k, A(1 + ... + 1) (n 1's) is provable in k steps, then (?x)A(x) is provable.