Definition:Gödel's Beta Function

Definition
Gödel's $\beta$ function $\beta: \N^3 \to \N$ is defined as:
 * $\map \beta {x, y, z} = \map {\operatorname{rem} } {x, 1 + \paren {z + 1} \times y}$

where $\operatorname{rem}: \N^2 \to \N$ is defined as:


 * $\map \rem {n, m} = \begin{cases}

\text{the remainder when } n \text{ is divided by } m & : m \ne 0 \\ 0 & : m = 0 \end{cases}$

Also see

 * Gödel's Beta Function is Arithmetically Definable
 * Gödel's Beta Function Lemma