论文标题
半连接的摩根单型和赋形剂
Semilinear De Morgan monoids and epimorphisms
论文作者
论文摘要
证明了（i）半线性，即完全有序代数的细分产物，以及（ii）产生的，即由中性元素的下限产生的负面产生的de Morgan Monoids的表示定理。使用该定理，我们证明了De Morgan Monoids满足（I）和（ii）形成了局部有限的品种。然后，我们证明，在各种负面产生的半线性de Morgan单型中，表达是汇总的。在此过程中，还为其他几个类别建立了表达解释率，包括所有半决赛的多样性交换晶格的种类和所有负面产生的半线性邓恩单型胶状的品种。结果解决了有关贝丝风格的一系列副结构逻辑的自然问题。
A representation theorem is proved for De Morgan monoids that are (i) semilinear, i.e., subdirect products of totally ordered algebras, and (ii) negatively generated, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.
