Should a published paper with a published correction be replaced on arXiv? I submitted a paper to a journal.  It was accepted and published.
I had also posted a version of the paper on arXiv.  The arXiv version of the paper and the journal's version are not identical, because the journal's version uses their house LaTeX style.  However, the two versions are otherwise the same, and share the same theorem numbering.
Then someone pointed out an error in the paper.  So I wrote a short correction, and submitted it to the journal.  It has been accepted and published as a separate paper.
My question is: what should I do with the arXiv version of the paper?  Here are some possibilities.


*

*Replace the version on arXiv with a new version, which incorporates the necessary changes into the paper.  Doing so would probably change the theorem numbering, so that it does not agree with the original paper.

*Post the correction to the arXiv as a separate paper, and leave the old arXiv version of the original paper alone (so that it still agrees with the published version).

*Post the correction to arXiv as a separate paper, and to replace the original paper on arXiv with a new version, which incorporates footnotes pointing out the erroneous statements, and referencing the correction (but otherwise not changing theorem numbering).
The third choice seems like the right one to me.  But I'd like to know what the accepted practice is here (if there is one).
Added.  Several answers suggest a fourth choice:
4. Replace the original paper on arXiv with a revised version, but make sure the revision does not change theorem numbering, or at least carefully indicate the changes in numbering.  
Added.  The consensus seems to be for choice 4.  This is what I'll do, since it looks like I'll be able to keep the numbering the same.
 A: You could post a new version where you have attached the correction to the paper (I thought this could be done automatically when updating papers on the arXiv?). This way, you keep the numbering, and people who look for the original paper will find the update as well. 
A: In any case I think you should update the arXiv paper, that's where most people will read your paper anyways. Besides, writing a separate errata paper seems a bit unnecessary in this case. In the arXiv version you could probably add a footnote about the change of numbering. 
On the other hand, when people reference a result our article, it would be convenient if the numbering is the same in both versions. Would it be possible to change the theorem numbering in the arXiv paper so that it resembles the submitted version?
A: The theorem-numbering is irrelevant - re-write the paper and re-post on the ArXiv; the best version of your paper is then right there front and center. Old version are kept there as well, so if someone is reading a reference to the old version of your paper they can look it up easily enough (and if someone has been sloppy enough to reference an ArXiv paper without mentioning the version, well, shame on them).  
A: Probably there are also ways to force LaTeX to renumber the new theorems in such a way as it doesn't conflict with the old numbering.  (Theorem 6.3B or something similar, or perhaps have the added theorems with their own numbering system using a different counter, roman numerals or something?)
A: I'd be inclined to use option 1.  If I correctly understand the arXiv's policies, the old version will remain available anyway.  You could include in the new version a footnote indicating which arXiv version corresponds to the published version.  If you're really worried about the changed theorem numbers, a "reader's guide" to the changes could be included either as a footnote in the new arXiv version or as an arXiv comment.
