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| title = Proceedings of the International Congress of Mathematicians, 1958
| contribution-url = http://www.mathunion.org/ICM/ICM1958/Main/icm1958.0289.0299.ocr.pdf
| year = 1960}}.</ref> which is the [[proof-theoretic ordinal]] of [[Peano arithmetic]]. PRA's proof theoretic ordinal is ω<sup>ω</sup>, where ω is the smallest [[transfinite number|transfinite ordinal]]. PRA is sometimes called '''Skolem arithmetic'''.
The language of PRA can express arithmetic propositions involving [[natural number]]s and any [[primitive recursive function]], including the operations of [[addition]], [[multiplication]], and [[exponentiation]]. PRA cannot explicitly quantify over the ___domain of natural numbers. PRA is often taken as the basic [[metamathematic]]al [[formal system]] for [[proof theory]], in particular for [[consistency proof]]s such as [[Gentzen's consistency proof]] of [[first-order arithmetic]].
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