Division by zero

• Published in 2016
• Added on 2016-04-26

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.

Links

• http://arxiv.org/abs/1604.07309
• http://arxiv.org/pdf/1604.07309v1

Other information

BibTeX entry

@article{Jerabek2016,
	key = {Jerabek2016},
	type = {article},
	title = {Division by zero},
	author = {Emil Je{\v{r}}{\'{a}}bek},
	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 = {},
	date_added = {2016-04-26},
	date_published = {2016-04-01},
	urls = {http://arxiv.org/abs/1604.07309,http://arxiv.org/pdf/1604.07309v1},
	collections = {About proof},
	url = {http://arxiv.org/abs/1604.07309 http://arxiv.org/pdf/1604.07309v1},
	urldate = {2016-04-26},
	year = 2016,
	month = {apr},
	pages = 12,
	archivePrefix = {arXiv},
	eprint = {1604.07309},
	primaryClass = {math.LO}
}