I want to create a counter that enumerates the Theorem-environments and Definition- environments in a beamer presentation in such a way that the enumeration follows the section numbers (the first theorem in section 5 should be Theorem 5.1 etc.). These enumerations should be independent of one another (the first definition in section 5 should be Definition 5.1 and not Definition 5.2). Is there a way to do this?

\documentclass[9pt,trans,xcolor={table},envcountsect]{beamer} % Plain

\usefonttheme[onlymath]{serif}
\usetheme[shownavsym,right]{Aalborg}

\setbeamertemplate{section in toc}[sections numbered] % Automatic enumeration of sections
\setbeamertemplate{blocks}[rounded][shadow=true] 

\definecolor{dgreen}{rgb}{0.,0.6,0.} 
\definecolor{aaublue}{RGB}{33,26,82}% dark blue

\usepackage{etoolbox} % In order to still use an outdated beamer version

\AtBeginEnvironment{theorem}{%
\setbeamertemplate{itemize items}[circle]                    % Shape of bullet-points
\setbeamercolor{block title}{bg=dgreen!100!white,fg=white}%
\setbeamercolor{itemize item}{fg=dgreen!100!white}%
\setbeamercolor{itemize subitem}{fg=dgreen!100!white}%
\setbeamercolor{itemize subsubitem}{fg=dgreen!100!white}%
\setbeamercolor{enumerate item}{fg=dgreen!100!black}%
\setbeamercolor{enumerate subitem}{fg=dgreen!100!black}%
\setbeamercolor{enumerate subsubitem}{fg=dgreen!100!black}%
}

\AtBeginEnvironment{definition}{%
\setbeamertemplate{itemize items}[circle]                    % Shape of bullet-points
\setbeamercolor{block title}{bg=blue,fg=white}%
\setbeamercolor{itemize item}{fg=blue}%
\setbeamercolor{itemize subitem}{fg=blue}%
\setbeamercolor{itemize subsubitem}{fg=blue}%
\setbeamercolor{enumerate item}{fg=blue}%
\setbeamercolor{enumerate subitem}{fg=blue}%
\setbeamercolor{enumerate subsubitem}{fg=blue}%
}

\setbeamercolor*{block body}{bg=black!10!white,fg=black} 
\setbeamercolor*{block body alerted}{bg=normal text.bg!90!black,fg=black} 
\setbeamercolor*{block body example}{bg=normal text.bg!90!black,fg=black} 
\setbeamercolor*{block title}{parent=structure2,bg=normal text.bg!0!blue}
\setbeamercolor*{block title alerted}{use={normal text,alerted text},fg=alerted text.fg!0!white,bg=normal text.bg!10!red}
\setbeamercolor*{block title example}{use={normal text,example text},fg=white,bg=cyan}
\setbeamercolor*{block title theorem}{use={normal text,example text},fg=example text.fg!100!normal text.fg,bg=normal text.bg!0!dgreen}

\makeatletter
\pgfdeclareverticalshading[lower.bg,upper.bg]{bmb@transition}{200cm}{color(0pt)=(lower.bg); color(4pt)=(lower.bg); color(4pt)=(upper.bg)}
\makeatother

\makeatletter
\newcommand{\ShiftSectionNumber}[1]{%
\beamer@tocsectionnumber=\numexpr#1+\beamer@tocsectionnumber}
\makeatother

\setbeamertemplate{theorem begin}[normal font]

\begin{document}

\begin{frame}%[allowframebreaks]
    \frametitle{Overview}
    \tableofcontents
\end{frame}

\ShiftSectionNumber{4}
\addtocounter{section}{4} % Enumeration of theorems and examples follows section numbers

\section{Section}
\begin{frame}[<+->]{Enumeration of environments}
    \begin{theorem}[Wanted: Counter]
        \begin{itemize}
            \item Wanted: Counter that follows section numbers (Theorem 5.1)
        \end{itemize}     
    \end{theorem}
    \begin{theorem}[Wanted: Counter]
        \begin{itemize}
            \item Wanted: Counter that follows section numbers (Theorem 5.2)
        \end{itemize}     
    \end{theorem}
    \begin{definition}[Wanted: Counter]
        \begin{itemize}
            \item Wanted: Counter independent of theorem-counter: Definition 5.1
        \end{itemize}        
    \end{definition}
\end{frame}

\end{document}

>Solution :

\documentclass[9pt,trans,xcolor={table},envcountsect]{beamer} % Plain

\usefonttheme[onlymath]{serif}
\usetheme[shownavsym,right]{Aalborg}

\setbeamertemplate{section in toc}[sections numbered] % Automatic enumeration of sections
\setbeamertemplate{blocks}[rounded][shadow=true] 

\definecolor{dgreen}{rgb}{0.,0.6,0.} 
\definecolor{aaublue}{RGB}{33,26,82}% dark blue

\usepackage{etoolbox} % In order to still use an outdated beamer version

\AtBeginEnvironment{theorem}{%
\setbeamertemplate{itemize items}[circle]                    % Shape of bullet-points
\setbeamercolor{block title}{bg=dgreen!100!white,fg=white}%
\setbeamercolor{itemize item}{fg=dgreen!100!white}%
\setbeamercolor{itemize subitem}{fg=dgreen!100!white}%
\setbeamercolor{itemize subsubitem}{fg=dgreen!100!white}%
\setbeamercolor{enumerate item}{fg=dgreen!100!black}%
\setbeamercolor{enumerate subitem}{fg=dgreen!100!black}%
\setbeamercolor{enumerate subsubitem}{fg=dgreen!100!black}%
}

\AtBeginEnvironment{definition}{%
\setbeamertemplate{itemize items}[circle]                    % Shape of bullet-points
\setbeamercolor{block title}{bg=blue,fg=white}%
\setbeamercolor{itemize item}{fg=blue}%
\setbeamercolor{itemize subitem}{fg=blue}%
\setbeamercolor{itemize subsubitem}{fg=blue}%
\setbeamercolor{enumerate item}{fg=blue}%
\setbeamercolor{enumerate subitem}{fg=blue}%
\setbeamercolor{enumerate subsubitem}{fg=blue}%
}

\setbeamercolor*{block body}{bg=black!10!white,fg=black} 
\setbeamercolor*{block body alerted}{bg=normal text.bg!90!black,fg=black} 
\setbeamercolor*{block body example}{bg=normal text.bg!90!black,fg=black} 
\setbeamercolor*{block title}{parent=structure2,bg=normal text.bg!0!blue}
\setbeamercolor*{block title alerted}{use={normal text,alerted text},fg=alerted text.fg!0!white,bg=normal text.bg!10!red}
\setbeamercolor*{block title example}{use={normal text,example text},fg=white,bg=cyan}
\setbeamercolor*{block title theorem}{use={normal text,example text},fg=example text.fg!100!normal text.fg,bg=normal text.bg!0!dgreen}

\makeatletter
\pgfdeclareverticalshading[lower.bg,upper.bg]{bmb@transition}{200cm}{color(0pt)=(lower.bg); color(4pt)=(lower.bg); color(4pt)=(upper.bg)}
\makeatother

\makeatletter
\newcommand{\ShiftSectionNumber}[1]{%
\beamer@tocsectionnumber=\numexpr#1+\beamer@tocsectionnumber}
\makeatother

\setbeamertemplate{theorems}[numbered]
\addtobeamertemplate{theorem begin}{\normalfont}

\let\definition\undefined
\newtheorem{definition}{\translate{Definition}}[section]


\begin{document}

\begin{frame}%[allowframebreaks]
    \frametitle{Overview}
    \tableofcontents
\end{frame}

\ShiftSectionNumber{4}
\addtocounter{section}{4} % Enumeration of theorems and examples follows section numbers



\section{Section}
\begin{frame}[<+->]{Enumeration of environments}
    \begin{theorem}[Wanted: Counter]
        \begin{itemize}
            \item Wanted: Counter that follows section numbers (Theorem 5.1)
        \end{itemize}     
    \end{theorem}
    \begin{theorem}[Wanted: Counter]
        \begin{itemize}
            \item Wanted: Counter that follows section numbers (Theorem 5.2)
        \end{itemize}     
    \end{theorem}
    \begin{definition}[Wanted: Counter]
        \begin{itemize}
            \item Wanted: Counter independent of theorem-counter: Definition 5.1
        \end{itemize}        
    \end{definition}
\end{frame}

\end{document}