Timeline for Are $\mathbb C$ , $\mathbb C[X]$ definable in $\mathbb C[[X]]$?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 7, 2018 at 20:18 | vote | accept | CommunityBot | ||
| Mar 7, 2018 at 20:18 | vote | accept | CommunityBot | ||
| Mar 7, 2018 at 20:18 | |||||
| Mar 6, 2018 at 19:49 | answer | added | Will Sawin | timeline score: 11 | |
| Mar 1, 2018 at 15:30 | comment | added | Emil Jeřábek | There is also vast literature on quantifier elimination in henselian valued fields (or valuation rings, for that matter), which I am mostly unfamiliar with, but very likely some of it can be applied here. | |
| Mar 1, 2018 at 15:26 | comment | added | Emil Jeřábek | Hmm. So, that means the question is cross-posted from math.stackexchange.com/questions/2667763/… . | |
| Mar 1, 2018 at 15:10 | comment | added | user111524 | @EmilJeřábek: But even that might not be so easy ... see math.stackexchange.com/questions/2669359/… and math.stackexchange.com/questions/2669549/… | |
| Mar 1, 2018 at 15:06 | comment | added | Emil Jeřábek | Nevertheless, I think that some kind of automorphism argument might work. In particular, since $\mathbb C$ has infinite transcendence degree, I would expect that even if you fix finitely many parameters, there should be an automorphism of $\mathbb C[[X]]$ that moves some element of $\mathbb C$ outside $\mathbb C[X]$. | |
| Mar 1, 2018 at 15:02 | comment | added | user111524 | @EmilJeřábek : Exactly ... thank you for getting my point ... I also explained this in my comment above | |
| Mar 1, 2018 at 15:00 | comment | added | Emil Jeřábek | @PiotrAchinger Note that the OP is interested in definability with parameters. Your argument is blocked if you take e.g. $X$ as a parameter. | |
| Mar 1, 2018 at 14:09 | comment | added | Piotr Achinger | The answer to the second question is no: pick any power series $Y = X + \ldots$, then there is an automorphism of $\mathbb{C}[[X]]$ sending $X$ to $Y$, and hence $\mathbb{C}[X]$ to $\mathbb{C}[Y]$. | |
| Mar 1, 2018 at 13:43 | history | asked | user111524 | CC BY-SA 3.0 |