论文标题
通过自动形态组测试理论的定义等效性
Testing definitional equivalence of theories via automorphism groups
论文作者
论文摘要
当且仅当其模型类之间存在双构象类别以保存同构和超副措施（定理2）时，两种一阶逻辑理论在定义上是等效的。这是Van Benthem和Pearce先前定理的变体。在示例2中，给出了许多定义上不相等的理论，以使其模型类别通过在模型类别中保留超强的双构型具有同构的同构，直到同构。基于这些结果，我们解决了Barrett，Glymour和Halvorson的几个猜想。
Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, Glymour and Halvorson.
