Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to ε₀, which is the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is ωω, where ω is the smallest transfinite ordinal. PRA is sometimes called Skolem arithmetic.ᵂᴾ
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Onstage he was known for ricochet riffs on politics, social issues and cultural matters both high and low; tales of drug and alcohol abuse; lewd commentaries on relations between the sexes; and lightning-like improvisations on anything an audience member might toss at him.
