Division by zero

Emil Jeřábek

doi:10.1007/s00153-016-0508-5

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arXiv · 1604.07309

Division by zero

Emil Jeřábek

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Abstract

For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show 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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Emil Jeřábek. 2016-04-25. Division by zero. https://doi.org/10.1007/s00153-016-0508-5

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