Multiple lists of theorems with different titles (any TeX, in my case XeLaTeX)

Question

I've found out how to use the thmtools package to make lists of theorems. My questions on this are:

1. How do I change the title, given that \renewcommand{\listoftheoremname}{...} gives a LaTeX error: \listoftheoremname undefined error?
2. How do I make multiple lists of different kinds of theorems with different titles?

3. Adding [name=xxx,label=thm:...] after \begin{yyy} (xxx is a title for the theorem, ... a label appearing in the list, yyy the theorem kind) labels a theorem. If I try to put any maths beyond superscript and subscript (for now I've only tried \mathbb) into a label, I get a missing \endcsname inserted error related to a line of the .aux files. How do I solve that? MWE:

   \documentclass[a4paper]{report}  
   \usepackage{thmtools,amssymb}  
   \declaretheorem[name=Definizione]{defi}  
   \begin{document}  
   \begin{defi}[name=$\mathbb R$,label=thm:$\mathbb R$definizione]  
   Ah beh, s\`i beh.  
   \end{defi}  
   \listoftheorems  
   \end{document}  
   

which gives:
.
The same error is obtained by placing a \ref in a label. In fact, \mathbb gives problems anywhere in those [], just like trying to put $(0,1)$ there, because of that comma.

4. (should be 4) And finally, I'm using theorems with [subsection] numbering. Now, in the list, the number overlaps the theorem kind (i.e. I get 1.2.1.1 overlapping Definizione (Spazio Metrico)). How do I solve that?

Answer 1

This could get you started; but without a clear set of specifications from you it's difficult to be more precise.

\documentclass{article}
\usepackage{amsthm,thmtools}

\declaretheorem{theorem}
\declaretheorem[style=definition]{definition}

\begin{document}

\renewcommand{\listtheoremname}{List of theorems}
\listoftheorems[ignoreall,show=theorem]

\renewcommand{\listtheoremname}{List of definitions}
\listoftheorems[ignoreall,show=definition]

\begin{theorem}[Sum]
$1+1=2$
\end{theorem}

\begin{definition}[Nice numbers]
A number is \emph{nice} if it looks beautiful.
\end{definition}

\begin{theorem}[About $C^{1}(0,1)$]
The set $C^{1}(0,1)$ is interesting.
\end{theorem}

\end{document}