M. Coste, H. Lombardi, and M.F. Roy, Dynamical methods in algebra: eective Nullstellensatze, Annals of Pure and Applied Logic 111(3):203{ 256, 2001.  Home/Search   Document Not in Database   Summary   Related Articles

....theory above is actually two sorted. It would be possible to consider as well multisorted geometric logic. This is not strictly necessary, since the usual reduction to one sort, using unary predicates Line and Point and relativizing the quanti ers, results in a one sorted geometric theory. In [3], the notion of geometric theory is extended by function symbols and equations on these symbols. A typical axiom is the theory of elds, with function symbols for additions and products, with the usual equational axioms for rings and the geometric axiom x = 0 (9y) x y = 1) The rst order ....

....a 2 , and adding the facts S a 0 a 1 ; S a 0 a 2 . The proof obligation is then At each step in the proof procedure, only a nite number of parameters are alive (as in [7] We then collect all facts that we can derive using the Horn part Such a separation of the theory appears both in [12] and [3]. In [12] this is used to prove that Desargues Theorem is independent of the theory of projective geometry presented above. 10 of the theory. In the example of the theory NL, only a 0 ; a 1 ; a 2 are alive at rst and from the facts S a 0 a 1 ; S a 0 a 2 we can only derive S a 0 a 0 ; E a 0 a 0 ....

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M. Coste, H. Lombardi, and M.F. Roy, Dynamical methods in algebra: eective Nullstellensatze, Annals of Pure and Applied Logic 111(3):203{ 256, 2001.

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