 Next one applies this to two fields, one given by an ultraproduct over all primes of the fields F"p"(("t")) and the other given by an ultraproduct over all primes of the "p"-adic fields "Q""p".Both residue fields are given by an ultraproduct over the fields F"p", so are isomorphic and have characteristic 0, and both value groups are the same, so the ultraproducts are elementarily equivalent.