From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener) Newsgroups: sci.math,sci.logic Subject: Re: Undecidable Diophantine equation Date: 2 Jun 1998 21:09:16 GMT In article , tchow@lsa (Timothy Chow) writes: >People have written down explicit Diophantine polynomial equations whose >solubility is undecidable in ZFC (assuming ZFC is consistent). I wanted >to show such an equation to a (non-mathematician) friend of mine, and I >thought I had saved a copy somewhere but I can't find it. Could someone >please email me an example (or a reference)? In view of the audience, >the simpler the example the better. J P Jones "Undecidable Diaphontine Equations" BULL AMS (NS), v3, pp 859-862, 1980. J P Jones "Universal Diaphontine Equation" JOUR SYMB LOGIC v47, pp 549-571, 1982. My memory is clear only regarding the explicit universal equation being written out (in the BAMS announcement). It is an equation of the form P(a,b,c,d,...,y,z)=0 such that by choosing a,b,c (to A,B,C, say), one has the sets { z | (E d,e...y) P(A,B,C,d,e,...,y,z)=0 } ranging over precisely the recursively enumerable sets. Obviously, for certain choices of a,b,c, then, one has an undecidable Diaphontine equation. I do not recall if Jones did this last step explicitly or not. -- -Matthew P Wiener (weemba@sagi.wistar.upenn.edu)