Talk:Primitive recursive arithmetic

History

History: Skolem (1923) the first published version.

Say sth about the possibility of presenting PRA in a logic-free equation calculus? (Propositional connectives can be replaced with pr functions.) 131.111.8.102 09:07, 25 August 2007 (UTC)

Left turn

Article takes a huge left turn at the logic-free calculus section, by using a formalism that is not explained, and apparently not even linked to the article. This is, indeed, a calculus which is free from logic! 70.247.164.231 (talk) 21:26, 28 August 2010 (UTC)

Perhaps this helps? The big horizontal bar is the Rule of inference -- 67.198.37.16 (talk) 20:47, 8 July 2016 (UTC)

From $\phi (0)$ and $\phi (x)$ $\to$ $\phi (S(x))$, deduce $\phi (y)$, for any predicate $\phi .$

What do you mean by "predicate" here? You don't mention above, that in the language of PRA predicate symbols exist. Perhaps you mean "formula of PRA"? Eugepros (talk) 10:48, 21 July 2011 (UTC)

Yeah, beats me, this looks like either a mistake or something that needs clarification and explanation. Or something. 67.198.37.16 (talk) 20:55, 8 July 2016 (UTC)

Skolem arithmetic ?

Could anyone give a citation where PRA is called Skolem Arithmetic ? As far as I can tell, everytime I read "Skolem Arithmetic" in a mathematical article, it means the logic with multiplication on positive number, without addition.

Hence, this redirection seems really wrong to me. — Preceding unsigned comment added by Arthur MILCHIOR (talk • contribs) 12:18, 27 June 2012 (UTC)

WP currently has this solution to this question: Skolem arithmetic (disambiguation). 67.198.37.16 (talk) 20:33, 8 July 2016 (UTC)

Unfolding

It would be nice to add a discussion of unfolding (logic) and how it connects finitist arithmetic to PRA and non-finitist arithmetic to Peano arithmetic, as discussed by Feferman, Strahm Unfolding finitist arithmetic (2010) but as can be seen, the various red-links make this currently quite difficult. 67.198.37.16 (talk) 20:31, 8 July 2016 (UTC)