# Division by zero

- Published in 2016
- Added on

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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.

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- pages
- 12

### BibTeX entry

@article{Jerabek2016, title = {Division by zero}, author = {Emil Je{\v{r}}{\'{a}}bek}, url = {http://arxiv.org/abs/1604.07309 http://arxiv.org/pdf/1604.07309v1}, urldate = {2016-04-26}, year = 2016, 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.}, comment = {}, month = {apr}, pages = 12, archivePrefix = {arXiv}, eprint = {1604.07309}, primaryClass = {math.LO}, collections = {About proof} }