论文标题
关于比较数学结构量的自动形态标准
On Automorphism Criteria for Comparing Amounts of Mathematical Structure
论文作者
论文摘要
Wilhelm（2021）最近为比较数学对象的结构进行了辩护，他称之为亚组。他认为，亚组比Sym *更好，这是另一个广泛采用的标准。我们认为这是错误的。亚组严格比sym *差。然后，我们制定了一个新的标准，该标准对Sym *和子组都改进，回答了Wilhelm对Sym *的批评。我们结论说，没有一个仅考虑数学对象的自动形态以比较其结构的标准，这是完全令人满意的。
Wilhelm (2021) has recently defended a criterion for comparing structure of mathematical objects, which he calls Subgroup. He argues that Subgroup is better than SYM * , another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM *. We then formulate a new criterion that improves on both SYM * and Subgroup, answering Wilhelm's criticisms of SYM * along the way. We conclude by arguing that no criterion that looks only to the automorphisms of mathematical objects to compare their structure can be fully satisfactory.
