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...
| Publicado en: | Synthese Vol. 199; no. 3/4; pp. 6357 - 6370 |
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| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Dec2021
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| 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. |
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