Decidable Fragment of Theories in Field Arithmetic
Chun-Yu Lin · arXiv (Cornell University) · 2019
In this paper, we show that the $\exists^1 \forall^1$ theories of Hilbertian fields with charateristic 0 and perfect Hilbertian fields are both decidable. We also prove that the $\forall^1 \exists^1$ theories of Hilbertian fields with charateristic 0, Hilbertian fields, PAC fields with characteristic 0, and PAC fields are all decidable.