# Existential rank and essential dimension of diophantine sets

@inproceedings{Daans2021ExistentialRA, title={Existential rank and essential dimension of diophantine sets}, author={Nicolas Daans and Philip Dittmann and Arno Fehm}, year={2021} }

We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points associated to such a definition.

## 2 Citations

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with 32 unknowns

- Mathematics
- 2021

Let Z be the ring of integers. Hilbert’s Tenth Problem (HTP), the tenth one of his 23 famous mathematical problems presented in the 1900 ICM, asks for an algorithm to determine for any given…

NOTES ON THE DPRM PROPERTY FOR LISTABLE STRUCTURES

- MathematicsThe Journal of Symbolic Logic
- 2021

Abstract A celebrated result by Davis, Putnam, Robinson, and Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic.…

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NOTES ON THE DPRM PROPERTY FOR LISTABLE STRUCTURES

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Abstract A celebrated result by Davis, Putnam, Robinson, and Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic.…

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