160

## 縮寫

$$()$$
$$0$$
$$\textbf{四}(s,t)$$
($$(s,t) \in T^2$$)
$$\textbf{四}_s(t)$$
$$\textbf{四}_0(t)$$
($$t \in T$$)
$$\textbf{四}(t)$$
$$\textbf{四}(0)$$
$$1$$
$$1+1$$
$$2$$
$$2+1$$
$$3$$
$$\textbf{四}(1)$$
$$\omega$$
$$\textbf{四}_1(0)$$
$$\Omega$$
$$(2,v),s_0,s_1$$
($$(v,s_0,s_1) \in T^3)$$
$$v,s_0,s_1$$
$$(3,v),s_0,s_1$$
($$(v,s_0,s_1) \in T^3)$$
$$v,0,s_0,s_1$$
$$(u_0,v_0),\ldots,(u_n,v_n),s_0,s_1$$
($$n \in \mathbb{N}, (u_0,\ldots,u_n,v_0,\ldots,v_n,s_0,s_1) \in T^{2n+4})$$
$$\begin{array}{ccccc} v_0 & \cdots & v_n & s_0 & s_1 \\ u_0 & \cdots & u_n & 1 & 0 \end{array}$$
$$(1,0,1),s_0,s_1$$
($$(s_0,s_1) \in T^2)$$
$$\begin{array}{cccccc} 1 & s_0 & s_1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}$$
$$\textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right)$$
$$M$$
$$(1,0,1),(u_0,v_0).\ldots,(u_n,v_n),s_0,s_1$$
($$n \in \mathbb{N}, (u_0,\ldots,u_n,v_0,\ldots,v_n,s_0,s_1) \in T^{2n+5})$$
$$\begin{array}{cccccc} 1 & v_0 & \cdots & v_n & s_0 & s_1 \\ 0 & u_0 & \cdots & u_n & 1 & 0 \\ 1 & 0 & \cdots & 0 & 0 & 0 \end{array}$$

## 解析

$$t \in OT$$ $$\textrm{ot}(t) \in \omega_1^{\textrm{CK}}$$
$$0$$
$$0$$
$$1$$
$$1 := \varphi_0(0)$$
$$2$$
$$2 := 1+1$$
$$3$$
$$3 := 2+1$$
$$\omega$$
$$\omega := \varphi_0(1)$$
$$\textbf{四}(\omega)$$
$$\varphi_0(\omega)$$
$$\textbf{四}(\Omega)$$
$$\varphi_1(0)$$
$$\textbf{四}(\Omega+\Omega)$$
$$\varphi_1(1)$$
$$\textbf{四}(\textbf{四}_1(1))$$
$$\varphi_1(\omega)$$
$$\textbf{四}(\textbf{四}_1(\Omega))$$
$$\varphi_2(0)$$
$$\textbf{四}(\textbf{四}_1(\textbf{四}_1(1)))$$
$$\varphi_{\omega}(0)$$
$$\textbf{四}(\textbf{四}_1(\textbf{四}_1(\Omega)))$$
$$\psi_{\chi_0(0)}(0)$$
$$\textbf{四}(\textbf{四}_2(0))$$
$$\psi_{\chi_0(0)}(\varphi_1(\chi_0(0)+1))$$
$$\textbf{四}(\textbf{四}_3(0))$$
$$\psi_{\chi_0(0)}(\varphi_1(\chi_0(1)+1))$$
$$\textbf{四}(\textbf{四}_{\omega}(0))$$
$$\psi_{\chi_0(0)}(\chi_0(\omega))$$
$$\textbf{四}(\textbf{四}_{\omega}(1))$$
$$= \textbf{四}(\textbf{四}(\textbf{季} 0))$$
$$\psi_{\chi_0(0)}(\varphi_0(\chi_0(\omega)+1))$$
$$\textbf{四}(\textbf{四}(1,0,0))$$
$$\psi_{\chi_0(0)}(\Phi_1(0))$$
$$\textbf{四}(\textbf{四}(2,0,0))$$
$$\psi_{\chi_0(0)}(\Phi_1(\chi_1(0)+1))$$
$$\textbf{四}(\textbf{四}(3,0,0))$$
$$\psi_{\chi_0(0)}(\Phi_1(\chi_1(1)+1))$$
$$\textbf{四}(\textbf{四}(1,0,0,0))$$
$$\psi_{\chi_0(0)}(\psi_{\chi_2(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ \omega & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\omega}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{ccc} 1 & \omega & 1 \\ \omega & 1 & 0 \end{array} \right) \right)$$
$$= \textbf{四}(\textbf{四}(\textbf{季} 1))$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\omega}(0)}(0) + \varphi_0(\chi_{\omega}(0)+1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ \Omega & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\chi_0(0)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ \textbf{四}_2(0) & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\psi_{\varphi_1(\chi_0(0)+1)}(0)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ \textbf{四}_{\omega}(0) & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\psi_{\chi_{\omega}(0)}(0)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ \textbf{四}(1,0,0) & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\Phi_1(0)}(0)}(0))$$
$$\textbf{四}(M)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M}(0)}(0))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M}(0)}(0)+\psi_{\chi_{M}(0)}(0))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 1 \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_0(\psi_{\chi_{M}(0)}(0)+1))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_0(\psi_{\chi_{M}(0)}(0)+\psi_{\chi_{M}(0)}(0)))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & 0 \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_1(\psi_{\chi_{M}(0)}(0)+1))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & 0 \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_2(\psi_{\chi_{M}(0)}(0)+1))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \omega \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_{\omega}(\psi_{\chi_{M}(0)}(0)+1))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & 0 \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_0(\chi_{M}(0)+1)}(0))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & \textbf{四} \left( \begin{array}{ccc} 1 & 1 & 0 \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_0(\chi_{M}(0)+1)}(0))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 2 & 0 & 0 \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M}(0)}(1))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} \omega & 0 & 0 \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M}(0)}(\omega))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M & 1 & 0 \end{array} \right) & 0 & 0 \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M}(0)}(\psi_{\chi_{M}(0)}(0)))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M+1 & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\chi_{M}(0))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M+2 & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M+1}(0)}(0))$$
$$\textbf{四} \left( M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M + \textbf{四} \left( \begin{array}{ccc} 1 & 0 & 0 \\ M & 1 & 0 \end{array} \right) & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M+\psi_{\chi_{M}(0)}(0)}(0)}(0))$$
$$\textbf{四}(M+M)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{M+M}}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_0(M+1)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & M \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_0(M+M)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_0(\varphi_0(M+1))}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_1(M+1)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_2(M+1)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_{\omega}(M+1)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & M \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_M(1)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & M+1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\psi_{\chi_{\varphi_{M+1}(0)}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(M)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + 1 \right)$$
$$\varphi_0(\psi_{\chi_0(0)}(M)+1)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \Omega \right)$$
$$\varphi_1(\psi_{\chi_0(0)}(M)+1)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\Omega) \right)$$
$$\varphi_2(\psi_{\chi_0(0)}(M)+1)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,1)) \right)$$
$$\varphi_{\omega}(\psi_{\chi_0(0)}(M)+1)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\Omega)) \right)$$
$$\psi_{\chi_0(0)}(M+1)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\Omega)+1) \right)$$
$$\psi_{\chi_0(0)}(M+\omega)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\Omega)+\Omega) \right)$$
$$\psi_{\chi_0(0)}(M+\chi_0(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\Omega)+\textbf{四}(1,\Omega)) \right)$$
$$\psi_{\chi_0(0)}(M+\varphi_0(\chi_0(0)+\chi_0(0)))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\Omega+1)) \right)$$
$$\psi_{\chi_0(0)}(M+\varphi_0(\varphi_0(\chi_0(0)+1)))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\Omega+\Omega)) \right)$$
$$\psi_{\chi_0(0)}(M+\varphi_0(\varphi_0(\chi_0(0)+\chi_0(0))))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(1,\textbf{四}(1,1))) \right)$$
$$\psi_{\chi_0(0)}(M+\varphi_0(\varphi_0(\varphi_0(\chi_0(0)+1))))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,\textbf{四}(2,0)) \right)$$
$$\psi_{\chi_0(0)}(M+\varphi_1(\chi_0(0)+1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(2,0) \right)$$
$$\psi_{\chi_0(0)}(M+\chi_0(1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四}(1,0,0) \right)$$
$$\psi_{\chi_0(0)}(M+\chi_1(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 0 \\ \omega & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(M+\psi_{\chi_{\omega}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 0 \\ M & 1 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(M+\psi_{\chi_{M}(0)}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + M \right)$$
$$\psi_{\chi_0(0)}(M+M)$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_0(M+1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & M \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_0(M+M))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_0(\varphi_0(M+1)))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_1(M+1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_2(M+1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_{\omega}(M+1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & M \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_{M}(1))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & M+1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_{M+1}(0))$$
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) + \textbf{四} \left( \begin{array}{cccccc} 1 & 0 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
$$\psi_{\chi_0(0)}(\varphi_{\varphi_{\cdot_{\cdot_{\cdot_{\varphi_{M+1}(0)}\cdot}\cdot}\cdot}(0)}(0))$$
$$=$$ $$\psi$$的可算限界
$$\textbf{四} \left( \textbf{四} \left( \begin{array}{cccccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right) \right)$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,1),2,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,1),\omega,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,1),(2,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,1),(\omega,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,1),(M,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,1),(\textbf{四}(((2,1),0,1),(M,1),0,0),1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),0,2),0,0))$$
?
$$\textbf{四}(\textbf{四}(((2,1),1,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((2,2),0,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((3,1),0,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((\omega,1),0,1),0,0))$$
?
$$\textbf{四}(\textbf{四}(((\omega,1),\omega,1),\omega,1))$$
$$= \textbf{四}(\textbf{四}(\textbf{季} 2))$$
?
$$\textbf{四}(\textbf{四}((((\omega,1),\omega,1),\omega,1),\omega,1))$$
$$= \textbf{四}(\textbf{四}(\textbf{季} 3))$$
?
$$\Omega$$
?
$$\textbf{四}(\omega,1)$$
$$= \textbf{四}(\textbf{季} 0)$$
?
$$\textbf{四} \left( \begin{array}{ccc} 1 & \omega & 1 \\ \omega & 1 & 0 \end{array} \right)$$
$$= \textbf{四}(\textbf{季} 1)$$
?
$$\textbf{四}(((\omega,1),\omega,1),\omega,1)$$
$$= \textbf{四}(\textbf{季} 2)$$
?
$$\textbf{四}((((\omega,1),\omega,1),\omega,1),\omega,1)$$
$$= \textbf{四}(\textbf{季} 3)$$
?
$$\textbf{四} \underbrace{(((((\cdots),\omega,1),\omega,1),\omega,1),\omega,1)}_{n+1}$$ ($$n \in \mathbb{N}$$)
$$= \textbf{四}(\textbf{季} n)$$
?