Create a copy of the subsections counter

Question

I'm writing a mathematics paper with \documentclass{amsart}, and I would like my theorems, definitions, propositions, etc., to be numbered "like subsections", i.e., if a given theorem is the fourth in section 3, it should be called Theorem 3.4.

The usual way to do this seems to be the following:

\newtheorem{theorem}[subsection]{Theorem} \newtheorem{proposition}[subsection]{Proposition} \newtheorem{definition}[subsection]{Definition} ...

That is, the counter used by the theorem, proposition, definition, etc environments is the default subsection counter.

The problem with this, however, is that it interferes with subsection numbering. For example:

1. Suppose that I'm in section 3.
2. Then, I start a subsection, which is appropriately called section 3.1.
3. Then, the first theorem I type will be called 3.2, but since it is actually the first theorem in section 3, I feel it should be called theorem 3.1.
4. If, after that, I start another subsection, it will be called section 3.3, but since it is the second subsection, I feel it should be called section 3.2 instead... and so on.

The solution I imagined for this was to create another counter that works exactly like subsection but independent of it, but I have failed to do this. I am only able to create new counters that use one number, not "nested" counters, like subsection or subsubsection, if that makes any sense. Any help in doing that or other solutions to my problem would be greatly appreciated.

Answer 1

Probably you want something like

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition} 
\newtheorem{definition}[theorem]{Definition}

That is number theorem within section and the others to follow the same numberation of theorem

MWE

\documentclass{amsart}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition} 
\newtheorem{definition}[theorem]{Definition}

\begin{document}
\section{A section}
\subsection{A subsection}
\begin{theorem}
A theorem
\end{theorem}
\begin{proposition}
A proposition
\end{proposition}
\subsection{Another subsection}
\begin{definition}
A definition
\end{definition}
\end{document} 

If you, instead, want different counters for different types of theorems, use

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{definition}{Definition}[section]

MWE

\documentclass{amsart}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{definition}{Definition}[section]

\begin{document}
\section{A section}
\subsection{A subsection}
\begin{theorem}
A theorem
\end{theorem}
\begin{proposition}
A proposition
\end{proposition}
\subsection{Another subsection}
\begin{definition}
A definition
\end{definition}
\end{document}