Quantifier elimination on some pseudo-algebraically closed valued fields
Logic
2022-07-29 v1
Abstract
Adjoining to the language of rings the function symbols for splitting coefficients, the function symbols for relative -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.
Keywords
Cite
@article{arxiv.1801.00226,
title = {Quantifier elimination on some pseudo-algebraically closed valued fields},
author = {Jizhan Hong},
journal= {arXiv preprint arXiv:1801.00226},
year = {2022}
}