论文标题
方程定义的半群类别
Equationally defined classes of semigroups
论文作者
论文摘要
我们在半群的背景下应用了〜\ cite {higjac}的主要定理，即代数的基本类$ \ mathcal {c} $，该代数是在采集直接产品和同质图像下封闭的，由方程式定义。我们证明了Birkhoff定理的双重双重，因为如果在包含半群中也关闭了班级，则$ \ MATHCAL {C} $方程的某些依据不含$ \ forall $量词。给出了EHP类别的示例，这些EHP级需要在任何方程式的某个方程式中需要两个以上的量词。
We apply, in the context of semigroups, the main theorem from~\cite{higjac} that an elementary class $\mathcal{C}$ of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We prove a dual to the Birkhoff theorem in that if the class is also closed under the taking of containing semigroups, some basis of equations of $\mathcal{C}$ is free of the $\forall$ quantifier. Examples are given of EHP-classes that require more than two quantifiers in some equation of any equational basis.
