Re: Provable in T?

Aatu Koskensilta wrote:
MoeBlee wrote:
Okay, that's one point I've always wondered about. But what is, in a
sense, the weakest theory to which the first incompleteness theorem
applies? Is it again ISigma_1 arithmetic? (That's the question I really
meant.)

The first incompleteness theorem applies to much weaker theories,
including Robinson arithmetic. I don't think there is any theory that is
in any sense the weakest to which the first incompleteness theorem
applies, but of the natural theories Robinson arithmetic or one of its
variants would probably come close.

Good, thanks, that's what I wanted to know.

MoeBlee

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