Abstract.
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 \(k\), \(A(1 + \cdots + 1)\) (\(n\) 1's) is provable in \(k\) steps, then \((\forall x)A(x)\) is provable.
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Received: February 1, 1996
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Baaz, M., Zach, R. Note on generalizing theorems in algebraically closed fields. Arch Math Logic 37, 297–307 (1998). https://doi.org/10.1007/s001530050100
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DOI: https://doi.org/10.1007/s001530050100