Talk:Primitive recursive arithmetic

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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)[reply]

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)[reply]

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)[reply]

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)[reply]

History

Left turn

From ϕ ( 0 ) {\displaystyle \phi (0)} and ϕ ( x ) {\displaystyle \phi (x)} → {\displaystyle \to } ϕ ( S ( x ) ) {\displaystyle \phi (S(x))} , deduce ϕ ( y ) {\displaystyle \phi (y)} , for any predicate ϕ . {\displaystyle \phi .}

Skolem arithmetic ?

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