NOTE ON GENERALIZING THEOREMS IN ALGEBRAICALLY CLOSED FIELDS

Authors
BAAZ M ZACH R
Citation
M. Baaz et R. Zach, NOTE ON GENERALIZING THEOREMS IN ALGEBRAICALLY CLOSED FIELDS, Archive for mathematical logic, 37(5-6), 1998, pp. 297-307
Citations number
5
Categorie Soggetti
Mathematics,Mathematics
Journal title
Archive for mathematical logic → ACNP
ISSN journal
09335846
Volume
37
Issue
5-6
Year of publication
1998
Pages
297 - 307
Database
ISI
SICI code
0933-5846(1998)37:5-6<297:NOGTIA>2.0.ZU;2-P
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 A CF(p) admits finite term bases, and ACF(0) admits term bases with prim ality constraints. From these results the analogs of Kreisel's Conject ure for these theories follow: If for some k, A(1 +...+ 1) (n l's) is provable in k steps, then (For All x)A(x) is provable.