Submission date: 31 December 2017.

Abstract:

Adjoining to the language of rings the function symbols for splitting coefficients, the function symbols for relative p-coordinate functions, and the division predicate for a valuation, some theories of pseudo-algebraically closed non-trivially valued fields admit quantifier elimination. It is also shown that in the same language the theory of pseudo-algebraically closed non-trivially valued fields of a given exponent of imperfection does not admit quantifier elimination, due to Galois theoretic obstructions.

Mathematics Subject Classification:

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Full text arXiv 1801.00226: pdf, ps.