论文标题
逻辑和代数的代数扩展以及Abelian L组和完美MV代数的案例研究
Algebraic expansions of logics and algebras and a case study of Abelian l-groups and perfect MV-algebras
论文作者
论文摘要
代数可扩展（AE）类是一类代数结构，可通过$ \ forall \ forall \ for的句子的句子进行公理化！ \ Land P = Q $。对于由Quasivariety $ \ Mathcal {q} $构建的逻辑$ L $代数，我们表明$ \ Mathcal {Q} $的Ae-Subclasses对应于$ L $的某些自然扩展，我们称为{\ em em eLgebraic Expansions}。事实证明，这些是X. Caicedo研究的隐式连接剂的特殊情况。我们开始表征Abelian $ \ ell $ -groups和Perfect MV-Algebras的所有AE-SUBLASSE，从而充分描述了其相关逻辑的代数扩展。
An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \land p = q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AE-subclasses of $\mathcal{Q}$ correspond to certain natural expansions of $L$, which we call {\em algebraic expansions}. These turn out to be a special case of the expansions by implicit connectives studied by X. Caicedo. We proceed to characterize all the AE-subclasses of Abelian $\ell$-groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics.
