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I just have a question which may not be of much importance, but just curious. We have Zorn's lemma, Schur's lemma, Gauss's theorem, Cayley's theorem, Poincare lemma, Gauss lemma, Hilbert basis theorem, and Noether theorem.

I note that when a name is put in front of the theorem or lemma, there sometimes appear their possessives but sometimes not. Above the first four do while the last four don't. Is this just a convention? For example I never heard some one said Zorn lemma...

By the way, I am also confused that if I have to put "the" before the name. At first I think it should be but sometimes ignored in the titles. However, I still seldom heard some one say "the" Zorm's lemma...

Any ideas are appreciated!

User
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  • Lots of examples of both usages at https://en.wikipedia.org/wiki/List_of_theorems. – lhf Apr 19 '17 at 01:57
  • Oh... so just up to the writer? – User Apr 19 '17 at 02:07
  • Just up to the writer, or, maybe more often, the one who most notably uses the result in a published work. I think most of us have an informal priority: Theorem $>$ Proposition $>$ Lemma, but any two people place the inequality signs differently among various results. – Lubin Apr 19 '17 at 02:13

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