I am using the revtex4 package and wanted to change the section numbers to arabic for all levels. Furthermore, I wanted the sections to be displayed as 1.2. (as opposed to 2. only).
I only use sections and subsections, so I did the following:
\def\thesection{\arabic{section}}
\def\thesubsection{\thesection.\arabic{subsection}}
Now the sections and subsections are displayed how I want them. However, referencing subsections is now broken. It displays like this (edited example):
\documentclass[twocolumn,pre,floats,aps,amsmath,amssymb,a4,floatfix]{revtex4}
\usepackage{acronym}
\usepackage[english]{babel}
\setcounter{secnumdepth}{3}
\pagenumbering{arabic}
\def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\begin{document}
\section{First Section}
\subsection{A Subsection}
\label{sub:example}
And then some text.
\section{Second Section}
Let's ref Section \ref{sub:example}.
\end{document}

... instead of 1.1.
I see two resolutions, but don't know how to go about any of them:
Change the display numbers of sections in a smarter way, OR
Change what \ref displays (so that it displays only the subsection when subsections are referenced.
How can I achieve any of these, or is there another way?

