Re: Independent independence

aatu.koskensilta@xxxxxxxxx wrote:
Herman Jurjus wrote:
Is there already an example known of a theorem for which the statement
expressing its independence from ZFC is itself independent from ZFC?

"ZFC is consistent" is such an example -- as is anything independent
of ZFC, as it happens. I suspect you're not asking the question you
really have in mind.

Ah - well, finding exact formulations which make the question non-trivial is the crucial part of answering the question, i'd say.

Obviously, the question becomes trivial if you think of 'the statement expressing independence' as something like:
'ZFC |/- A and ZFC |/- -A'.
But the statements proved in the usual independence proofs (of CH, AC
etc.) are all (afaik) of the form:
'if ZF is consistent, then so are ZF + A and ZF + -A'.

Do we know an A for which -that- sentence is provably independent from ZFC?

--
Cheers,
Herman Jurjus

.

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