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arXiv · 1801.00226

Quantifier elimination on some pseudo-algebraically closed valued fields

Jizhan Hong
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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.

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Jizhan Hong. 2017-12-31. Quantifier elimination on some pseudo-algebraically closed valued fields. https://doi.org/10.1016/j.apal.2022.103170

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