The language of PRA can express arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation.

Nov 17, 2025 · PRA can express arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation.

Peano - (1889) The principles of arithmetic presented by a new method (He used recursive de nitions and induction. Next we look at primitive recursive de nitions of numerical functions.)

PRA's primary goal is to axiomatize precisely those total computable functions definable via primitive recursion—such as addition and exponentiation —without encompassing the full class of total …

Mar 14, 2025 · Goodstein's "Recursive Number Theory" (1957) presents a "logic-free" version of primitive recursive arithmetic: all statements in the logic are equalities of expressions involving …

We have seen that basic arithmetic functions such as addition, multiplication and proper subtraction are all primitive recursive. In fact, it is quite dificult to come up with an arithmetic function that fails to be …

We proved this already, by showing that the primitive recursive functions are Turing computable, and the Turing computable functions are definable by bounded formulas.

4.1 Primitive Recursive Functions Summary 4.1.1 In this section we consider a noteworthy subclass of computable functions, the class of primitive recursive functions.

Primitive recursive arithmetic (PRA), a formal axiom system for the natural numbers and the primitive recursive functions on them, is often used for this purpose.

Jun 15, 2025 · Primitive Recursive Arithmetic (PRA) is a fundamental formal system in mathematical logic that plays a crucial role in the foundations of mathematics. At its core, PRA is concerned with …