Timeline for Matching power series to infinity
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 22, 2015 at 20:38 | comment | added | Pace Nielsen | That will also work. There is no obstacle in that construction (other than finding the appropriate monoid $I$ corresponding to the choice axiom you want). | |
| Jan 22, 2015 at 20:20 | comment | added | Noah Schweber | I was thinking in a slightly different direction: off the top of my head, I think we have a reasonable ring of power series for any index set $I$ which is the underlying set of a monoid $(I, *)$ such that for each $x$ in $I$, there are only finitely many pairs $y_1, y_2$ with $y_1*y_2=x$. But maybe there's another obstacle? | |
| Jan 22, 2015 at 20:15 | comment | added | Pace Nielsen | The construction I'm familiar with (namely, the Malcev-Neumann series) depends on supports which are well-ordered. So while you can get more general equivalences, I believe there may be some natural (algebraic) limitations. | |
| Jan 22, 2015 at 19:40 | comment | added | Noah Schweber | Actually, note that this establishes an equivalence: the statement "if every coefficient of the powerseries is a multiple of $c$, then the series is a multiple of $c$" is equivalent (over ZF) to the axiom of countable choice. And, if we generalize the class of formal power series to index sets other than $\omega$ in the natural way, we get equivalences with other forms of choice, too. | |
| Jan 22, 2015 at 18:28 | comment | added | Pace Nielsen | This is what I thought must happen. Glad to see a quick answer. (This, of course, answers all the other more complicated questions as well.) | |
| Jan 22, 2015 at 18:28 | vote | accept | Pace Nielsen | ||
| Jan 22, 2015 at 18:17 | history | answered | Noah Schweber | CC BY-SA 3.0 |