How to refer to a theorem that you have shown to be wrong I am writing a paper about a flaw that I found in a published paper. There, the statement is called “Theorem 2”. In my paper, I am reproducing the other paper’s definitions, and steps leading towards that statement, and now I’d like to reproduce the statement, immediately followed by the counter example that I found.
I am tempted to reproduce the statement labelled and styled as a theorem in my paper as well, so that the reader can easily find and recognize it, and so that I can continue to refer to it as “Theorem 2”. But is that really valid, given that only correctly proven statements are, by definition of theorem, theorems? Or can there be such things as “false theorems“?
 A: Another example is the paper "Affine semigroups and Cohen-Macaulay rings" by Hoa and Trung (Trans. AMS 298, 1986) in which they give a counterexample to a result of Goto and Watanabe.  Rumor has it that the counterexample was known before their paper, but in any case, they use "counterexample to the result".
A: I once saw a mathematician giving a talk about a theorem that he thought he had proved, for which a counterexample had later been found. He stated the "result" as follows:
Theorem (1983–1987): Let $A$ be $\dots$
(I made up the dates of birth and death)
A: In my opinion, it would be a bad idea to label statements known to be false as theorems. If you really want to do this, maybe you could put inverted commas around the word "theorem", to indicate you explicitly cast doubt on its following from axioms by applying rules of deduction. Or you could call it an Assertion, followed by a bold declaration that the assertion is false and the demonstration of such. 
A: You can have a look to the paper "A counterexample to a 1961 “theorem” in homological algebra" by Neeman and use his style. By the way, I think that the paper is very very good.
A: It might be that the proof in the paper you refer to did not prove the whole claim, but proved something weaker but still nontrivial. (Imagine for example, a statement of the Weierstrass extreme value theorem without assuming that the domain is not empty. Probably the proof covers the non empty domain case.) In that case, I could try to state a theorem with the additional assumption and mention in a remark or in a footnote that the statement is weaker than the one in the source and that the assumption I have added was needed at some point in the proof I precise. 
By the way, when I find a counterexample to a published result, I find it a good practice to identify where the published proof is failing. (Most of the time, proofs fail in the parts left to the reader, but you can still find a counterexample to an intermediate statement in a proof.) 
