关于泛类的Blok-Esakia定理
On the Blok-Esakia theorem for universal classes
摘要：
Blok-Esakia定理指出，存在从中间逻辑格到Grzegorczyk模态逻辑的正规扩张格的同构。Emil Jeábek作为典范规则的一个应用得到了多结论推论关系的推广。我们表明，Jeanábek的结果如下已经从布洛克的代数证明。我们还证明了强结构完备性和强泛完备性的性质被保持并反映在上述同构中。这些性质分别与单结论推论关系的结构完备性和泛完备性相一致，特别是对于逻辑。
英文摘要：
The Blok-Esakia theorem states that there is an isomorphism from the lattice of intermediate logics onto the lattice of normal extensions of Grzegorczyk modal logic. The extension for multi-conclusion consequence relations was obtained by Emil Jeřábek as an application of canonical rules. We show that Jeřábek's result follows already from Blok's algebraic proof. We also prove that the properties of strong structural completeness and strong universal completeness are preserved and reflects by the aforementioned isomorphism. These properties coincide with structural completeness and universal completeness respectively for single-conclusion consequence relations and, in particular, for logics.
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