Timeline for Is there a polynomial equation whose solution over the integers is independent of ZFC
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2012 at 14:45 | vote | accept | Daniel Bachmat | ||
| Apr 28, 2012 at 14:45 | |||||
| Apr 28, 2012 at 14:12 | comment | added | Joel David Hamkins | Yes, one can write down explicit diophantine equations with the property. For any computably axiomatizable formal system $T$, there is a diophantine equation whose solutions are the Goedel codes of a proof of a contradiction in $T$. If $T$ is consistent, this diophantine equation will have no solution, but $T$ will be unable to prove this. (About your inquiry about more powerful systems, follow the link in my comment to your question above, where this is discussed at length.) | |
| Apr 28, 2012 at 14:00 | comment | added | Daniel Bachmat | It is possible to construct such an equation? Does this mean that in more powerful systems we can solve the 10th problem? | |
| Apr 28, 2012 at 13:48 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |