On finite intersections of ?henselian valued? fields

Abstract

In this note we study finite intersections of “henselian valued” fields, i.e. fields carrying either a henselian valuation ring or a henselian absolute value which is (real-) archimedean. To be more precise, we intersect a finite number of henselian valued respectively real closed fields such that the induced valuation rings respectively orderings generate different V-topologies on the intersection, and investigate its algebraic and valuation-theoretic properties.