9,992 Pages

## First attempt

This part is wrong after (0,0,0)(1,1,1)(2,1,0).

### $$\psi(\Omega_\omega)$$ to TFB

(0,0,0)(1,1,1) has level $$\psi(\Omega_\omega)$$

(0,0,0)(1,1,1)(1,1,0) has level $$\psi(\Omega_\omega+1)$$

(0,0,0)(1,1,1)(1,1,0)(2,1,0) has level $$\psi(\Omega_\omega+\Omega)$$

(0,0,0)(1,1,1)(1,1,0)(2,2,0) has level $$\psi(\Omega_\omega+\psi_1(0))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1) has level $$\psi(\Omega_\omega+\psi_1(\Omega_\omega))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0) has level $$\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,2,0) has level $$\psi(\Omega_\omega+\Omega_2)$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,3,0) has level $$\psi(\Omega_\omega+\Omega_3)$$

(0,0,0)(1,1,1)(1,1,1) has level $$\psi(\Omega_\omega*2)$$

(0,0,0)(1,1,1)(2,0,0) has level $$\psi(\Omega_\omega*\omega)$$

(0,0,0)(1,1,1)(2,1,0) has level $$\psi(\Omega_\omega*\Omega)$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1) has level $$\psi(\Omega_\omega*\psi_1(\Omega_\omega))$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1)(3,2,1) has level $$\psi(\Omega_\omega*\psi_1(\Omega_\omega*2))$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,2,0) has level $$\psi(\Omega_\omega*\Omega_2)$$

(0,0,0)(1,1,1)(2,1,1) has level $$\psi(\Omega_\omega^2)$$

(0,0,0)(1,1,1)(2,1,1)(2,1,1) has level $$\psi(\Omega_\omega^3)$$

(0,0,0)(1,1,1)(2,1,1)(3,0,0) has level $$\psi(\Omega_\omega^\omega)$$

(0,0,0)(1,1,1)(2,1,1)(3,1,1) has level $$\psi(\Omega_\omega^{\Omega_\omega})$$

(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1) has level $$\psi(\Omega_\omega^{\Omega_\omega^2})$$

(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1,1) has level $$\psi(\Omega_\omega^{\Omega_\omega^{\Omega_\omega}})$$

### TFB to  $$\psi(\psi_I(0))$$

(0,0,0)(1,1,1)(2,2,0) has level TFB

(0,0,0)(1,1,1)(2,2,0)(2,2,0) has level $$\psi(\psi_\omega(1))$$

(0,0,0)(1,1,1)(2,2,0)(3,1,0) has level $$\psi(\psi_\omega(\Omega))$$

(0,0,0)(1,1,1)(2,2,0)(3,1,1) has level $$\psi(\psi_\omega(\Omega_\omega))$$

(0,0,0)(1,1,1)(2,2,0)(3,2,0) has level $$\psi(\Omega_{\omega+1})$$

(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,2,0) has level $$\psi(\Omega_{\omega+1}^{\Omega_{\omega+1}})$$

(0,0,0)(1,1,1)(2,2,0)(3,3,0) has level $$\psi(\psi_{\omega+1}(0))$$

(0,0,0)(1,1,1)(2,2,0)(3,3,1) has level $$\psi(\Omega_{\omega*2})$$

(0,0,0)(1,1,1)(2,2,0)(3,3,1)(4,4,0)(5,5,1) has level $$\psi(\Omega_{\omega*3})$$

(0,0,0)(1,1,1)(2,2,1) has level $$\psi(\Omega_{\omega^2})$$

(0,0,0)(1,1,1)(2,2,1)(2,2,0)(3,3,1)(4,4,1) has level $$\psi(\Omega_{\omega^2*2})$$

(0,0,0)(1,1,1)(2,2,1)(2,2,1) has level $$\psi(\Omega_{\omega^3})$$

(0,0,0)(1,1,1)(2,2,1)(3,0,0) has level $$\psi(\Omega_{\omega^\omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,0) has level $$\psi(\Omega_{\Omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,1) has level $$\psi(\Omega_{\Omega_\omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,1)(4,2,1) has level $$\psi(\Omega_{\Omega_{\omega^2}})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,1)(4,2,1)(5,1,1)(6,2,1) has level $$\psi(\Omega_{\Omega_{\Omega_{\omega^2}}})$$

### $$\psi(\psi_I(0))$$ to $$\psi_{I(\omega,0)}(0)$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0) has level $$\psi(\psi_I(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(3,2,0) has level $$\psi(\psi_I(1))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(3,3,0) has level $$\psi(\psi_{\Omega_{I+1}}(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(5,4,1)(6,4,0) has level $$\psi(\psi_{I_2}(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,1) has level $$\psi(\psi_{I_\omega}(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,1)(3,2,0)) has level $$\psi(\psi_{I(1,0)}(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)) has level $$\psi(\psi_{I(1,\omega)}(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,0)) has level $$\psi(\psi_{I(2,0)}(0))$$

### $$\psi_{I(\omega,0)}(0)$$ to $$\psi_{I(\varepsilon_{M+1},0)}(0)$$

(0,0,0)(1,1,1)(2,2,1)(3,2,1)(4,0,0)) has level $$\psi(\psi_{I(\omega,0)}(0))$$

## Second attempt

This is going to be a lot more complicated than I thought. The first part is a summer of Aarex's analysis.

(0,0,0)(1,1,1)(2,1,0)(1,1,1) has level $$\psi(\Omega_\omega^2)$$

(0,0,0)(1,1,1)(2,1,0)(2,1,0)(1,1,1) has level $$\psi(\Omega_\omega^3)$$

(0,0,0)(1,1,1)(2,1,0)(3,0,0) has level $$\psi(\Omega_\omega^\omega)$$

(0,0,0)(1,1,1)(2,1,0)(3,1,0) has level $$\psi(\Omega_\omega^\Omega)$$

(0,0,0)(1,1,1)(2,1,0)(3,2,0) has level $$\psi_{omega}(0)$$

(0,0,0)(1,1,1)(2,1,0)(3,2,0) has level $$\psi_{omega}(0)$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1) has level $$\psi(\Omega_{\omega*2})$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,1,0) has level $$\psi(\Omega_{omega*2}*\Omega)$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)(1,1,1) has level $$\psi(\Omega_{omega*2}*\Omega_\omega)$$