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Informally in mathematical logic, an algebraic theory is one that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Sentential logic is the subset of first-order logic involving only algebraic sentences. The notion is very close to the notion of Algebraic Structure, which, arguably, may be just a synonym. Saying that a theory is algebraic is a stronger condition than saying it is elementary. ==Informal Interpretation== An algebraic theory consists of a collection of ''n''-ary functional terms with additional rules (axioms). E.g. a group theory is an algebraic theory because it has three functional terms: a binary operation ''a * b'', a nullary operation ''1'' (neutral element), and a unary operation ''x'' → ''x−1'' with the rules of associativity, neutrality and inversion respectively. This is opposed to geometric theory which involves partial functions (or binary relationships) or existential quantors - see e.g. Euclidean geometry where the existence of points or lines is postulated. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「algebraic theory」の詳細全文を読む スポンサード リンク
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