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Erschienen in:
1991 | ReviewPaper | Buchkapitel
Complete axiomatizations of some quotient term algebras
verfasst von : Hubert Comon
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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We show that T(F)/ =E can be completely axiomatized when =E is a quasi-free theory. Quasi-free theories are a wider class of theories than permutative theories of [Mal71] for which Mal'cev gave decision results. As an example of application, we show that the first order theory of T(F)/ =E is decidable when E is a set of ground equations. Besides, we prove that the ∑1-fragment of the theory of T(F)/ =E is decidable when E is acompact set of axioms. In particular, the existential fragment of the theory of associative-commutative function symbols is decidable.