论文标题
完全代表的整洁还原
Completely representable neat reducts
论文作者
论文摘要
对于序数$α$，$ \ sfpea_α$表示尺寸$α$的多边形平等代数类别。我们表明，对于几类代数，这些代数为$ \pea_Ω$，其签名包含所有替换和有限的圆柱体，如果$ \ b $在这样的班级中，$ \ b $是原子，那么对于所有$ n <ω$，$ \ nr_n \ b $都是$ \ pea_n的代表。相反，我们表明，对于任何$ 2 <n <ω$，以及任何品种$ \ sf v $，在对角线免费圆柱代数与尺寸$ n $的quasipolyadic equbras之间，这是$ \ sf v $的完全代表代数的类别。
For an ordinal $α$, $\sf PEA_α$ denotes the class of polyadic equality algebras of dimension $α$. We show that for several classes of algebras that are reducts of $\PEA_ω$ whose signature contains all substitutions and finite cylindrifiers, if $\B$ is in such a class, and $\B$ is atomic, then for all $n<ω$, $\Nr_n\B$ is completely representable as a $\PEA_n$. Conversely, we show that for any $2<n<ω$, and any variety $\sf V$, between diagonal free cylindric algebras and quasipolyadic equality algebras of dimension $n$, the class of completely representable algebras in $\sf V$ is not elementary.
