Complete intersections in Stein manifolds

The purpose of this note is to prove some theorems on set theoretic complete intersections in Stein manifolds (or Stein spaces) which are analogous to results in affine algebraic geometry. Due to the Oka principle in Stein theory one gets stronger results. For example any locally complete intersection Y of dimension 3 in a Stein space X with dim X>2 dim Y is a set theoretic₆ complete intersection. A 4-dimensional submanifold of⁶ is a set theoretic complete intersection if sc₁²(Y)=0 for some integer s>0.Der erstgenannte Autor dankt der Alexander-von-Humboldt-Stiftung für ein Stipendium zu einem Gastaufenthalt an der Universität Münster