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An undecidability result for power series rings of positive characteristics. II. (English) Zbl 0664.03008
[For part I see ibid. 99, 364-366 (1987; Zbl 0639.03009).]
We prove that the existential problem for a power series ring over an integral domain of positive characteristic with a predicate which represents the powers of the indeterminate is undecidable. We prove the same result for any ring which is contained in a power series ring and contains the corresponding ring of polynomials.

MSC:
03B25 Decidability of theories and sets of sentences
12L05 Decidability and field theory
13F25 Formal power series rings
11U05 Decidability (number-theoretic aspects)
11D88 \(p\)-adic and power series fields
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