论文标题
生物学，双子和双解释性
Bicategories, Biequivalence, and Bi-Interpretability
论文作者
论文摘要
我们为连贯的一阶逻辑的语法类别和句法类别之间的对应关系提供了明确的对应关系，从而提供了双重解相关性的分类表征。这是通过在相干理论的生物学和（严格的）相干类别的（严格的）生物学之间创建双人间来完成的。虽然双子关系涉及更强大的平等性双重纠正性，但我们通过将其确切的句法类别的确切完整完成，以使两种理论一般可以双重解释获得必要和充分的条件。这些结果类似于一阶逻辑的熟悉片段，从而阐明了逻辑语法和句法类别之间的长期关系。
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of coherent theories and the (strict) bicategory of coherent categories. While the biequivalence concerns the stronger equality-preserving bi-interpretability, we use it to obtain a necessary and sufficient condition for two theories to be bi-interpretable in general, by relating the exact completions of their syntactic categories. These results extend analogously to familiar fragments of first-order logic, thereby clarifying the long-intuited relation between logical syntax and syntactic categories.
