Define a $f\in R_\beta$ if it satisfies one of the following:
$$f(\alpha)=\alpha+1\\f(0)=\gamma,f(\alpha)=\sup\{g(f(\delta)):\delta<\alpha\}\\f(0)=\gamma,f(\alpha)=\sup\{\varphi_\eta(g,f(\delta)):\delta<\alpha,\eta<\min\{\alpha,\omega^{\mathrm{CK}}_\phi\},\phi<\beta\}$$
where
$$\gamma\in l_\beta\\g\in R_\beta\\\varphi_\eta(g,\delta)=\begin{cases}\sup\{g(\varphi_\psi(g,\delta)):\psi<\eta\},&\eta>0\\\delta,&\eta=0\end{cases}\\l_0=\{0,1,2,3,\dots\}\\m_\beta=\bigcup_{\zeta<\beta}l_\zeta\\l_\beta(0)=m_\beta\cup\sup(m_\beta)\\l_\beta(n+1)=l_\beta(n)\cup\{f(\pi):\pi\in l_\beta(n),f\in R_\sigma,…
Two of the properties of the exterior product are the following:
Let $\psi_1, \ldots , \psi_k, n_1, \ldots , n_{\ell}\in V^{\star}$ then it holds that $$\left (\psi_1\land \ldots \land \psi_k\right )\land \left (n_1\land \ldots \land n_{\ell}\right )=\psi_1\land \ldots \land \psi_k\land n_1\la...
