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Note on generalizing theorems in algebraically closed fields

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


The generalization properties of algebraically closed fields ACFp of characteristic p > 0 and ACF0 of characteristic 0 are investigated in the sequent calculus with blocks of quantifiers. It is shown that ACFp 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.


Yehuda Rav (Mathematical Reviews 2000a:03057)

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