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I am not well educated in set theory. This is a question that I would love to read answers to from the many experts who populate MO. That said, good answers do not good questions make. That said, I don't think the question is far from a good one, and I would be eager to reopen it if there's some editing out the rumors.
Question 1 is very palatable. It partly duplicates http://mathoverflow.net/questions/29302/reasons-to-believe-vopenkas-principle-huge-cardinals-are-consistent, but there is more to say on the subject of inaccessible than the answers there which focus on much larger cardinals.
Experience tells us that question 2 is inappropriate for MO. There has already been a summary thread on this kind of questions.
Question 3 is debatable. It may be entertaining to speculate about the effect of such a proof, but this is likely to resemble talk of The Big One. The impact on set theory would be disastrous in an unprecedented way, but the impact on mathematics as a whole would be comparatively very small. It is unlikely that this question has any kind of definite answer.
at the risk of fanning flames, what is The Big One?
This is already posted on FOM.
@Will - actually I'm more familiar with the Californian reference, now that I'm reminded of it. Fires are a bigger problem here than waves.
The recent edit eliminated the former question 2, which was the most problematic part.
The edited question overlaps with a bunch of earlier questions:
We can gather a very decent answer to the question by assembling the answers to the above. However, I don't see any exact duplicates in this list.
User Tip. Google is often a much better search engine than the MO search box. The list above was quickly gathered from the search site:mathoverflow.net large cardinals.
site:mathoverflow.net large cardinals
That's for the community to decide. There are currently 3 votes to reopen; you need 5 votes to reopen the question.
Deleted 'duplicate', sorry.
@Quinn - one needs 3k rep to see the vote counts.
Edit: I have just cast the fifth vote.