Timeline for Is there a polynomial equation whose solution over the integers is independent of ZFC
Current License: CC BY-SA 3.0
5 events
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| Apr 29, 2012 at 14:56 | comment | added | Johannes Hahn | I just saw Asaf Karagila's comment. In one answer in that thread Merlin Carl is mentioned (which is the "friend of mine" I was talking about) and in another answer Vladimir Reshetnikov gives an explicit and (for me surprisingly) short polynomial. | |
| Apr 29, 2012 at 14:45 | comment | added | Johannes Hahn | In principle I suppose I could. ;-) The polynomials that I and Joel David Hamkins describe are obtainable by algorithmic procedures. It's a very boring thing to do, but in principle possible, even by hand. A friend of mine told me he once calculated a "small" polynomial that encodes $con(ZFC)$ (or was it $con(PA)$ ?) for his diploma thesis. If I remember correctly he said that only [some two-digit number] variables were necessary and the polynomial would fit on [one-digit number] pages if printed. I could ask him if you like. | |
| Apr 28, 2012 at 15:44 | comment | added | Paul Siegel | Given all of this, can you give an explicit example of a diophantine equation for which PA can't prove or disprove the existence of a solution? | |
| Apr 28, 2012 at 14:45 | vote | accept | Daniel Bachmat | ||
| Apr 28, 2012 at 13:49 | history | answered | Johannes Hahn | CC BY-SA 3.0 |