Problem with shared numbering of theorems, propositions, etc. by section, ignoring subsections

Question

I confess that even though I've used LaTeX quite a bit, I am very much a novice when it comes to actual knowledge of programming in the language. I will definitely learn more about it some day.

I have some trouble with theorem numbering. What I want is for all theorems, definitions, remarks, etc. to be numbered like section.# through all subsections as well, i.e.:

Section 1

Theorem 1.1

Subsection 1.1

Theorem 1.2

Definition 1.3

Remark 1.4

Section 2

Proposition 2.1

Subsection 2.1

Definition 2.2

etc...

I tried adjusting for this by setting the theorem counter to section, and then setting all the others to "follow" theorem, as suggested here. This resulted in:

Section 2 ...

...

Subsection 2.2

Remark 2.0.1

Remark 2.0.2

Definition 2.0.1

Thus both the numbering were separate, and I do not really know where the '0' comes from here. I am at subsection 2.2 so if anything it should be 2.2.1 etc., but what I want is two numbers, 2.#, and for it to ignore the sub and subsubsections.

I clearly do not understand how the numbering works, what I have at the moment is the below code, using \documentclass[12pt, a4paper]{article} and amsthm package. Perhaps setting new theorem styles messes this up, but I thought the counters was only set at \newtheorem. I've also tried looking through different guides and other questions such as this, and this, but they all seem to suggest doing more or less what I've done, I thought, but obviously I've done something wrong.

% Style for theorems, propositions, lemmas etc.
\newtheoremstyle{plain_rev}
  {12pt}   % Space above (default is \topset)
  {12pt}   % Space below (default is \topset)
  {\itshape}  % Body font
  {}          % Indent amount
  {\bfseries} % Theorem head font
  {.}         % Punctuation after theorem head
  {5pt plus 1pt minus 1pt} % Space after theorem head
  {}          % custom Theorem head spec

\theoremstyle{plain_rev}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}{Proposition}[theorem]
\newtheorem{lemma}{Lemma}[theorem]
\newtheorem{corollary}{Corollary}[theorem]

% Style for examples, definitions, remarks
\newtheoremstyle{exampstyle}
  {12pt} % Space above (default is \topset)
  {12pt} % Space below (default is \topset)
  {} % Body font
  {} % Indent amount
  {\bfseries} % Theorem head font
  {.} % Punctuation after theorem head
  {.5em} % Space after theorem head
  {} % Theorem head spec

\theoremstyle{exampstyle}
\newtheorem{definition}{Definition}[theorem]
\newtheorem{example}{Example}[theorem]
\newtheorem{remark}{Remark}[theorem]

So basically, I have two theorem styles, one for theorem/proposition style things in italics, and one for examples etc. I have only changed the spacing somewhat on both of them.

Question(s): How do I get the above desired numbering, and is this an ok way of numbering them (i.e. it's at least not "ugly" in some way)?

(I understand from e.g. this that shared numbering is fine and often preferred, but I am talking more about skipping subsection, and using only two numbers. All my professor asked was for them (thm, def, rem,etc.) to be numbered consecutively, shared, i.e. not separately.)

Answer 1

For sake of having the question answered : the

\newtheorem{definition}{Definition}[theorem]

part should be swapped to :

\newtheorem{definition}[theorem]{Definition}