Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
From: Mike Oliver (mike_lists_at_verizon.net)
Date: 01/29/05
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Date: Sat, 29 Jan 2005 16:15:51 -0600
mareg@mimosa.csv.warwick.ac.uk wrote:
> My impression is rather that most mathematicians prefer
> to assume AC (rather than not AC), because it results in cleaner statements
> of theorems, like every vector space has a basis. I generally assume and use
> AC myself, but that is not the same thing as believing that it is any more
> true than not AC. What I find surprising is that there are people who
> believe that it is either true or false, but they don't know which.
So do you have any names of people who think that?
I continue to think that far more common than the position you
mention in your last sentence -- and indeed the overwhelming
majority opinion among realists about sets -- is that AC is
really true.
Substitute "CH" for "AC" and yes, there are probably a
great many who think it's really true or really false, but
who have no strong expectation of ever finding out which.
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