Re: Provable in T?

Aatu Koskensilta wrote:
And should I take it that there's no common theory that is between Robinson
arithmetic and ISigma_1 in terms of strength?

There are any number of such theories, obtained e.g. by omitting some instances of the induction axiom schema for Sigma_1 formulas.

To be more informative: there are theories between Q and ISigma_1 in strength, e.g. weak fragments of arithmetic containing Q in which it is not provable that exponentiation is total. You'll find more information in the book _Metamathematics of First Order Arithmetic_ or in Buss's article _First-Order Proof Theory of Arithmetic_ in Handbook of Proof Theory, available on-line.

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Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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