Timeline for Are there examples of nonconstructive metaproofs?
Current License: CC BY-SA 3.0
5 events
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| Jun 9, 2011 at 10:21 | comment | added | Emil Jeřábek |
The quantifiers in the assumption of Jacobson’s theorem I have in mind are $\forall a\in R\,\exists n > 1\,a^n=a$. However, in order to express this in equational logic, the exponent has to be fixed, hence we only consider the corollary of the theorem with the stronger assumption $\exists n\,\forall a\,a^n=a$ (more precisely, for each particular constant $n$, we consider the theorem with assumption $\forall a\,a^n=a$).
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| Jun 8, 2011 at 21:49 | comment | added | Qiaochu Yuan | Do you have your quantifiers in the right order in that statement? There are two closely related theorems of Jacobson that look like this and I'm not sure which one you mean. | |
| Jun 8, 2011 at 19:19 | vote | accept | skeptical scientist | ||
| Jun 8, 2011 at 19:19 | comment | added | skeptical scientist | Great answer. But I would still be interested in more examples, if anyone has some more. | |
| Jun 8, 2011 at 15:58 | history | answered | Emil Jeřábek | CC BY-SA 3.0 |