High Quality Content by WIKIPEDIA articles! 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 ожудз finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to ?0, which is the proof-theoretic ordinal of Peano arithmetic PRA's proof theoretic ordinal is ??, where ? is the smallest transfinite ordinal PRA is sometimes called Skolem arithmetic.  Salomon2010 г Мягкая обложка, 112 стр ISBN 6130346743.