Talk:Omega fixed point

Wait - what? There is infinitely many fixed points of $$\alpha\rightarrow\omega_{\alpha}$$, this is only the first.

$$\psi_I(1)$$ (second omega fixed point) $$= sup\lbrace\psi_I(0)+1,\omega_{\psi_I(0)+1},\omega_{\omega_{\psi_I(0)+1}},...\rbrace$$

$$\psi_I(2)$$ (third omega fixed point) $$= sup\lbrace\psi_I(1)+1,\omega_{\psi_I(1)+1},\omega_{\omega_{\psi_I(1)+1}},...\rbrace$$

$$\psi_I(\omega)$$ (omegath omega fixed point) $$= sup\lbrace\psi_I(0),\psi_I(1),\psi_I(2),...\rbrace$$

$$\psi_I(\omega_1)$$ (first uncountable ordinal-th omega fixed point)

$$\psi_I(\psi_I(0))$$ (first omega fixed point-th omega fixed point)

$$\psi_I(\psi_I(psi_I(0)))$$ (first omega fixed point-th omega fixed point-th omega fixed point)

I don't understand how the $$\psi$$ function works beyond $$\psi(\varepsilon_{\Omega+1})$$, but it appears that the first fixed point of $$\alpha\rightarrow\psi_I(\alpha)$$ is $$\psi_I(I)$$.

99.185.0.100 19:05, August 7, 2015 (UTC)

Yay text after the signature!

Yay another signature!

99.185.0.100 19:05, August 7, 2015 (UTC)