Sala delle Riunioni (Dip. Matematica Applicata)
A valuation ring O of a field K is called "henselian" if every polynomial in one variable with coefficients from O that has a simple zero in the quotient of O w.r.t. its maximal ideal, has already a zero in K. Such henselian fields are for example local fields and all generalized power series fields. In all these examples the valuation ring O remains fixed under all field automorphisms from K. The reason for this is that O can be defined by a first order formula in the language of rings.