Re: CH yet again.

MoeBlee wrote: 
Bill Taylor wrote:

Now and again I propose the PoV that CH is both true and false,
depending on how it is worded, there being two non-equivalent ways
for this in ZF without choice.
Would you say what the two non-equivalent formulas are?

The formulations "c = aleph_1" and "every infinite set of reals is either countable or has the cardinality of the continuum" are not equivalent without choice. The first of these obviously implies the second, but for the other direction you need choice. I don't know whether this is what Bill had in mind.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.