TITLE: Theorem versus Proposition
QUESTION [62 upvotes]: As a non-native English speaker (and writer) I always had the problem of understanding the distinction between a 'Theorem' and a 'Proposition'. When writing papers, I tend to name only the main result(s) 'Theorem', any auxiliary result leading to this Theorem a 'Lemma' (and, sometimes, small observations that are necessary to prove a Lemma are labeled as 'Claim'). I avoid using the term 'Proposition'.
However, sometimes a paper consists of a number important results (which by all means earn to be called 'Theorem') that are combined to obtain a certain main result. Hence, another term such as 'Proposition' might come in handy, yet I don't know whether it suits either the main or the intermediate results.
So, my question is: When to use 'Theorem' and when to use 'Proposition' in a paper?

REPLY [2 votes]: Edmund Landau had theorems only, and otherwise nothing (when it comes to naming special statements which required a proof; there should be also definitions and axioms on the top of the theorems).
Irving Kaplansky liked the Landau's style, thus he did the same.
(I am missing many of my books; in the case of Landau, there was a 2-volume differential and integral calculus textbook CLASSIC; in the case of Kaplansky, I think it was a monograph on ring theory).
You may always emphasize important results in several ways, without putting down the other results. One may put a name of a theorem in parenthesis, just after Theorem nn or one may create a subsection which identify the theorem in the section title, e.g. Section 2.4 The fundamental Theorem of Algebra (while, inside the section, this theorem could be Theorem 72, with a sentence of an explanation preceding that theorem).