Re: The meaning of set?


Aatu Koskensilta wrote:
Rupert wrote:
The good thing about ZFC is that we have an algorithm for generating
all the sentences we accept as theorems.

Really? What is that algorithm?


What I have in mind is an algorithm for listing every theorem of ZFC.
Such an algorithm exists because this set is recursively enumerable.
One possible algorithm would be one which searched through every
possible string of symbols and determined whether or not it was a proof
in ZFC, and if so, label the last line of the proof as a theorem. This
algorithm would be non-terminating since it lists an infinite set of
sentences, but every theorem would be verified as such within a finite
amount of time.

I'm not sure what your concern is. Perhaps you find my use of the
phrase "the sentences we accept as theorems" to be imprecise. Or
perhaps you don't agree with my calling this an "algorithm" since it is
non-terminating.


--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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

.

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