• Corpus ID: 218571448

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

  title={A Note on Hilbert's "Geometric" Tenth Problem.},
  author={Brian Tyrrell},
  journal={arXiv: Logic},
  • B. Tyrrell
  • Published 20 September 2019
  • Mathematics
  • arXiv: Logic
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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