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*Archive for Mathematical Logic* **37** (1998) 297–307

(with Matthias Baaz)

The generalization properties of algebraically closed fields ACF_{p} of characteristic *p* > 0 and ACF_{0} of characteristic 0 are investigated in the sequent calculus with blocks of quantifiers. It is shown that ACF_{p} admits finite term bases, and ACF_{0} 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.

Yehuda Rav (Mathematical Reviews 2000a:03057)