The shortest single axioms for groups of exponent 4
نویسندگان
چکیده
منابع مشابه
The Shortest Single Axioms for Groups of Exponent 4
We study equations of the form (= x) which are single axioms for groups of exponent 4, where is a term in product only. Every such must have at least 9 variable occurrences, and there are exactly three such of this size, up to variable renaming and mirroring. These terms were found by an exhaustive search through all terms of this form. Automated techniques were used in two ways: to eliminate m...
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Groups are usually deened by means of three axioms|the associative law, the existence of an identity element, and the existence of an inverse to each element. For abelian groups, the commutative law is included as a fourth axiom. However, it is well known that groups (also abelian groups) can be deened with a single equation. In 7], Tarski presented the single axiom x ? (y ? (z ? (x ? y))) = z ...
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It has long been an open question whether the formula XCB = EpEEEpqErqr is, with the rules of substitution and detachment, a single axiom for the classical equivalential calculus. This paper answers that question affirmatively, thus completing a search for all such eleven-symbol single axioms that began seventy
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1995
ISSN: 0898-1221
DOI: 10.1016/0898-1221(94)00212-4