Decidable Fragment of Theories in Field Arithmetic
Abstract
In this paper, we show that the ∃1 ∀1 theories of Hilbertian fields with charateristic 0 and perfect Hilbertian fields are both decidable. We also prove that the ∀1 ∃1 theories of Hilbertian fields with charateristic 0, Hilbertian fields, PAC fields with characteristic 0, and PAC fields are all decidable.
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