Re: Looking for Undecidable Propositions in Systems without a certain amount of arthimetic.



herbzet wrote:

MoeBlee wrote:

On Aug 14, 2:29 pm, herbzet <herb...@xxxxxxxxx> wrote:

Right. You might call the system of only logical axioms "the empty
theory" or "the null theory" -- it's just validities, no contingent
formula are provable or refutable.

I know what you mean by that, but personally I wouldn't use the
terminology 'empty theory' since the theory, which is a certain set of
sentences, is not the empty set.

Well, it's empty of non-logical axioms. :)

Well, maybe there's a lot of distinct "theories" without non-logical
axiom. Is a theory a set of sentences closed under entailment "|="
or a set that's deductively closed "|-" ?

--
hz
.

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