Talk:List of statements undecidable in ZFC
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[edit] Remarks on assumptions used to prove independence
I've revised the paragraph on large cardinals. What it said before was true--ZFC can neither prove nor disprove the existence of large cardinals. However what the page said at the top was "assuming ZFC is consistent", which in context probably refers to statements that can be formally proved in ZFC+Con(ZFC), and it is not possible to prove in ZFC+Con(ZFC) that the existence of large cardinals is consistent. In some sense that's the whole point of large cardinals--they provide a scale by which to measure "consistency strength".
But I think maybe the premise of the page should be rethought. It's extremely arbitrary--especially when talking aobut results like these--to assume tacitly that what we can assert is just what's provable in ZFC, and then add "assuming ZFC is consistent" to bump it up to ZFC+Con(ZFC). There are quite a few interesting statements that are independent of ZFC, but to prove one direction or the other you need some large cardinal strength; these could naturally be included here. --Trovatore 16:13, 15 October 2005 (UTC)
