We develop an elimination theory
for addition and the Frobenius map over rings of polynomials. As a
consequence we show that if F is a countable, recursive and
perfect field of positive characteristic p, with decidable
theory, then the structure of addition, the Frobenius map
x→ xp and the property ‘x∈ F', over the ring of
polynomials F[T], has a decidable theory.
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