# A Note on Hilbert's "Geometric" Tenth Problem.

@article{Tyrrell2020ANO, title={A Note on Hilbert's "Geometric" Tenth Problem.}, author={Brian Tyrrell}, journal={arXiv: Logic}, year={2020} }

This paper explores the decidability of the existential theory of positive characteristic function fields in the "geometric" language of rings $\mathcal{L}_F = \{0, 1, +, \cdot, F\}$, with a unary predicate $F$ for nonconstant elements. In particular we are motivated by a question of Fehm on the decidability of $\mbox{Th}_{\exists}(\mathbb{F}_p(t); \mathcal{L}_F)$; equivalently, that of $\mbox{Th}_{\exists}(\mathbb{F}_p(t); \mathcal{L}_{\mbox{rings}})$ without parameters. We prove $\mbox{Th}_…

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