3 ms·
> Where is the cutoff Is there a reason to believe there is a "cutoff"? As in, do we know that if the undecidability property holds for some ring A, then it ho
by dooglius 2y ago
> Where is the cutoff
Is there a reason to believe there is a "cutoff"? As in, do we know that if the undecidability property holds for some ring A, then it holds for every subring of A?
- eru 2y agoI guess it depends a bit on what you mean by subring? If you go by the strict definition of subring, I'm not sure. But we probably also want to explore other constructions like quotient rings, where I know that we can say some things. Eg calculating modulo some (given fixed) integer is a quotient ring on the integers.
- dooglius 2y agoI mean it pretty loosely, I'm just trying to figure out what Mazur meant. The quote and reference to a cutoff seems to imply that solveability preserves some kind of structural partial order between Z and C, but it's not clear to me why one would expect that to be the case.