Timeline for redundant relations
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2013 at 11:23 | comment | added | François G. Dorais | Thanks @Stefan, that's what I thought. (And I just cleared my confusion, which was mostly due to lack of caffeine.) | |
| Sep 13, 2013 at 9:14 | comment | added | Stefan Kohl♦ | @FrançoisG.Dorais: A group is called 'linear' iff it embeds into ${\rm GL}(n,\mathbb{C})$ for some $n \in \mathbb{N}$. | |
| Sep 13, 2013 at 4:05 | comment | added | François G. Dorais | @BenjaminSteinberg: I'm still confused by your comment but I can't tell why. What is the definition of a linear group? | |
| Sep 13, 2013 at 1:24 | comment | added | Benjamin Steinberg | @JoelDavidHamkins, you cannot enumerate proofs when you restrict the class of groups you are looking at to linear (or finite) groups. We have left the varietal setting. There are consequences of relations that are true in all linear groups but not all groups. For example let <X|R> be a finite presentation of an infinite simple group. Then R implies x=1 in all linear groups for every x in X because no infinite fg simple group has a non-trivial finite dimensional rep. But of course x=1 is not a consequence of R in all groups so there is no equational proof. | |
| Sep 13, 2013 at 1:19 | comment | added | Joel David Hamkins | @BenjaminSteinberg, I'm confused by your comment, since if implication checking is co-re, then it would have to be decidable, since clearly implication checking is also ce by enumerating proofs. | |
| Sep 13, 2013 at 1:16 | comment | added | Benjamin Steinberg | @JoelDavidHamkins, the undecidability with respect to the implications of linear groups is a slightly different problem. Due to residual finiteness checking implications is co-re. I will say more in my answer. | |
| Sep 13, 2013 at 0:01 | comment | added | Joel David Hamkins | Yes, I agree. I meant only to point out that indeed it is undecidable in the general case, since the comments expressed some degree of uncertainty about this. | |
| Sep 12, 2013 at 23:55 | comment | added | Martin Brandenburg | This doesn't really address the question. The OP already noticed that the general case is hard/undecidable. But I think that the question deals with concrete cases. | |
| Sep 12, 2013 at 23:51 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 18 characters in body
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| Sep 12, 2013 at 23:33 | comment | added | Joel David Hamkins | I'm not sure how your context of having matrices affects the situation. | |
| Sep 12, 2013 at 23:32 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |