Numbering in theorems

Question

I would like to have the following numbering based only on the section number:

Section 1, Theorem 1.1, Example 1.2, Example 1.3, Corollary 1.4, Section 2, Theorem 2.1, etc...

How do I obtain this?

My current setup is

\documentclass[a4paper,8pt]{report}
\usepackage{amsmath}
\usepackage{amsthm}

\newtheoremstyle{break}
  {\topsep}{\topsep}%
  {\upshape}{}%
  {\bfseries}{}%
  {\newline}{}%
\theoremstyle{break}
  \newtheorem{teor}[section]{Teorema}
  \newtheorem{cor}[section]{Corollario}

I've only reported mythm and mycor as an example.

Here's what happens with

\chapter{} %Parte 1%
\section{}

\begin{teor}
\end{teor}
\begin{cor}
\end{cor}
\section{}
\section{}

Answer 1

You should use a trailing [section] optional argument for one of the statement types, and then define the others as sharing the same counter as the main one.

\documentclass[a4paper]{report}
\usepackage{amsmath}
\usepackage{amsthm}

\newtheoremstyle{break}
  {\topsep}{\topsep}%
  {\upshape}{}%
  {\bfseries}{}%
  {\newline}{}%

\theoremstyle{break}
\newtheorem{teor}{Teorema}[section]
\newtheorem{cor}[teor]{Corollario}

and similarly for the others.

If you want to remove the initial chapter number (but don't), add also

\renewcommand{\theteor}{\arabic{section}.\arabic{teor}}