6

I want theorems to be labeled of the form Part.Chapter.Section.number so I tried

\renewcommand{\thesection}{\Roman{part}.\thechapter.\arabic{section}} 
\newtheorem{book}{Theorem}[section]
\newtheorem{AddProp}[book]{Additive Property of Equality}
\begin{AddProp} Testing \end{AddProp}

But does what I want, but as a side effect it also changes the sections, is there a way to only change the theorem numbering?

6

To have your AddProp "theorem" numbered by section using Part.Chapter.Section.Number, you can use:

\newtheorem{book}{Theorem}[section]
\newtheorem{AddProp}[book]{Additive Property of Equality}
\renewcommand{\thebook}{\thepart.\thesection.\arabic{book}}

This will also reset your book counter after every new \section. Here's a minimal example showing the usage/output:

enter image description here

\documentclass{report}
\newtheorem{book}{Theorem}[section]
\newtheorem{AddProp}[book]{Additive Property of Equality}
\renewcommand{\thebook}{\thepart.\thesection.\arabic{book}}
\begin{document}
\setcounter{part}{3} \part{A part}
\setcounter{chapter}{4} \chapter{A chapter}
\setcounter{section}{12} \section{A section}
\begin{AddProp} Testing \end{AddProp}
\section{Another section}
\begin{AddProp} Testing \end{AddProp}
\end{document}​

If you wish to maintain this structure, but have the book counter only reset every \chapter, then you need to drop the [section] part from the definition of the book theorem, and add the counter reset to your book counter manually:

%...
\newtheorem{book}{Theorem}%[section]
\makeatletter\@addtoreset{book}{chapter}\makeatother
%...

This functionality is provided by the chngcntr package as well as amsmath via user-friendly macros. Since you're using amsbook, you could use \numberwithin{book}{chapter}. See Master and slave counters and perhaps Section numbering with chapter in amsbook.

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