Comparing the structures of mathematical objects.

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...

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Detalles Bibliográficos
Publicado en:Synthese Vol. 199; no. 3/4; pp. 6357 - 6370
Autor principal: Wilhelm, Isaac
Formato: Artículo
Publicado: Springer Nature Dec2021
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Acceso en línea:Ver este registro en EBSCOhost
Descripción
Sumario: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.