Timeline for Is there a "listable" structure of computable dimension $\omega$?
Current License: CC BY-SA 4.0
12 events
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| Nov 30, 2020 at 11:55 | comment | added | Emil Jeřábek | I don’t know where the “algebraic-systems” tag comes from, but this is nonstandard terminology, and the name of the tag is quite misleading, as in common terminology an “algebraic structure” is one with no relations, only functions. I corrected some of the weird terminology in the tag summary, which wrote “laws” for what algebraists call “operations”, and logicians call “functions”. (This is quite bizarre, actually. Presumably, someone backformed it from the archaic phrase “group law” meaning “a rule that defines a group operation”.) | |
| Nov 30, 2020 at 7:09 | vote | accept | Noah Schweber | ||
| Nov 30, 2020 at 6:39 | answer | added | Dan Turetsky | timeline score: 4 | |
| Nov 30, 2020 at 3:35 | comment | added | Noah Schweber | @DanTuretsky Yeah, it's a strong condition (supposed to be the analogue of productivity for sets) - which is why I was surprised to find that I couldn't construct a counterexample. | |
| Nov 30, 2020 at 3:33 | comment | added | Dan Turetsky | Oh, I missed that your productive function took an index for a computable set of names of structures, not just a finite set. | |
| Nov 30, 2020 at 3:11 | comment | added | Noah Schweber | @DanTuretsky The index the productive function spits out has to name a structure not computably isomorphic to any named in the list. | |
| Nov 30, 2020 at 2:49 | comment | added | Dan Turetsky | Why does listable contradict productivity? If the productive function gave an index from your list, you could use the recursion theorem to contradict it, but what if your productive function gives you a different sort of index? | |
| Nov 29, 2020 at 21:14 | comment | added | YCor | Thanks! I find it useful to gather a certain type of questions about general structures. | |
| Nov 29, 2020 at 21:13 | history | edited | YCor |
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| Nov 29, 2020 at 21:06 | comment | added | Noah Schweber | @YCor I do dislike that tag, but I agree that granting it in the first place it's appropriate for this question. I'd only remove it if it crowded out a tag I considered more appropriate. Feel free to add it. | |
| Nov 29, 2020 at 20:37 | comment | added | YCor | I believe the tag algebraic-systems would perfectly fit here but unfortunately I believe you wouldn't keep the tag. | |
| Nov 29, 2020 at 19:50 | history | asked | Noah Schweber | CC BY-SA 4.0 |