Primitive recursive arithmetic (PRA) is a quantifier-free formalization of the natural numbers. It was first proposed by Norwegian mathematician Skolem...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

any contradictions either. This other system, today called "primitive recursive arithmetic with the additional principle of quantifier-free transfinite...

mathematics (Simpson 2009). Elementary recursive arithmetic (ERA) is a subsystem of primitive recursive arithmetic (PRA) in which recursion is restricted...

IΣ1 of Peano arithmetic in which induction is restricted to Σ01 formulas. In turn, IΣ1 is conservative over primitive recursive arithmetic (PRA) for Π...

interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed...

mathematical theory often associated with finitism is Thoralf Skolem's primitive recursive arithmetic. The introduction of infinite mathematical objects occurred...

multiplication and equality. Primitive recursive arithmetic, a quantifier-free formalization of the natural numbers. True arithmetic, the statements true about...

is given by a primitive recursive relation (Smith 2007, p. 141). As such, the Gödel sentence can be written in the language of arithmetic with a simple...

example, in primitive recursive arithmetic any computable function that is provably total is actually primitive recursive, while Peano arithmetic proves that...