# Division by zero

• Published in 2016
As a consequence of the MRDP theorem, the set of Diophantine equations provably unsolvable in any sufficiently strong theory of arithmetic is algorithmically undecidable. In contrast, we show the decidability of Diophantine equations provably unsolvable in Robinson's arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophantine literature. We also axiomatize the universal fragment of Q in the process.

## Other information

pages
12

### BibTeX entry

@article{Jerabek2016,
title = {Division by zero},
author = {Je\vr{\'{a}}bek, Emil},
url = {http://arxiv.org/abs/1604.07309 http://arxiv.org/pdf/1604.07309v1},
abstract = {As a consequence of the MRDP theorem, the set of Diophantine equations provably unsolvable in any sufficiently strong theory of arithmetic is algorithmically undecidable. In contrast, we show the decidability of Diophantine equations provably unsolvable in Robinson's arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophantine literature. We also axiomatize the universal fragment of Q in the process.},
month = {apr},
pages = 12,
year = 2016,
archivePrefix = {arXiv},
eprint = {1604.07309},
primaryClass = {math.LO},
urldate = {2016-04-26}
}