QUANTIFIER ELIMINATION FOR HENSELIAN FIELDS RELATIVE TO ADDITIVE AND MULTIPLICATIVE CONGRUENCES

Several classes of henselian valued fields admit quantifier elimination relative to structures which reflect the additive and multiplicative congruences of the field. Value groups and residue fields may be viewed as reducts of these structures. A general theorem is given using the theory of tame extensions of henselian fields. Special cases like the case of p-adically closed fields and the case of henselian fields of residue characteristic 0 are discussed.