A popular method for comparing the structures of mathematical objects, which I call the ‘subset approach’, says that X has more structure than Y just in case X’s automorphisms form a proper subset of Y’s automorphisms. This approach is attractive, in part, because it seems to yield the right results in some comparisons of spacetime structure. But as I show, it yields the wrong results in a number of other cases. The problem is that the subset approach compares structure using automorphism sets. So a different approach is needed: structure should be compared using automorphism groups.

中文翻译：

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比较数学对象的结构

比较数学对象的结构，我称之为“子方法”的常用方法，说，X具有超过结构Ÿ以防万一X的同构形成的真子集Ÿ的同构。这种方法之所以具有吸引力，部分原因在于，它在时空结构的某些比较中似乎产生了正确的结果。但是，正如我所展示的，它在许多其他情况下也会产生错误的结果。问题在于，子集方法使用自同构集比较结构。因此需要一种不同的方法：应该使用自同构组来比较结构。