关于结构完备性与几乎结构完备性问题：一个多类问题的实例研究
On structural completeness vs almost structural completeness problem: A discriminator varieties case study
摘要：
我们研究以下问题：确定哪些几乎结构完备拟簇是结构完备的。我们提出了一个一般的解决方案，这个问题，然后在半简单的情况下的解决方案。作为一个结果，我们得到了一个结构完整的类簇的特征。逻辑中一个有趣的推论如下：设$L$是语言中一个相容的命题逻辑/演绎系统，其中包含用于真的公式，这是一个定理，而假的不是一个定理。还假定$L$具有由一个簇给出的适当语义。则$L$是结构完备的当且仅当它是极大的。所有这样的逻辑/演绎系统在结构上几乎是完整的。
英文摘要：
We study the following problem: Determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let $L$ be a consistent propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that $L$ has an adequate semantics given by a discriminator variety. Then $L$ is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.
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