User blog:Nayuta Ito/Pure Maltiplication OCF

Definition:

$$C_0(\alpha,\beta)=\{0,1\}\cup\alpha$$

$$C_{n+1}(\alpha,\beta)=\{\alpha\beta, \psi(\gamma) | \alpha,\beta \in C_n(\alpha,\beta}, \gamma<\beta \}$$

$$C(\alpha,\beta)=\cup_{n\in\mathbb{N}}C_n(\alpha,\beta)$$

$$\psi_{\alpha}(\beta)=\mathrm{min}(\gamma \not \in C(\alpha,\beta))$$