\documentclass[11pt,a4paper,cleardoublepage=empty,oneside]{book}
\makeatletter
\def\ps@headings{%
\let\@oddfoot\@empty
\def\@oddhead{{\slshape\rightmark}\hfil\thepage}%
\let\@mkboth\markboth
\def\chaptermark##1{%
\markright {{% %%% original \MakeUppercase
\ifnum \c@secnumdepth >\m@ne
\@chapapp\ \thechapter. \ %
\fi
##1}}}}
\makeatother
\pagestyle{headings}
\usepackage{setspace}
\usepackage{array}
\usepackage{covington}
\usepackage[danish,english]{babel}
\usepackage{natbib}