Defectless polynomials over henselian fields and inductive valuations

Abstract Let ( K , v ) be a henselian valued field. Let P dless ⊂ K [ x ] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation  ≈  on P dless , we establish a canonical bijection M → P dless / ≈ , where M is a discrete MacLane space, constructed in terms of inductive valuations on K [ x ] extending v.