User blog:Nayuta Ito/A new ordinal notation in which ω 1 is countable

As you know,

\(\epsilon_{\alpha} = \varphi(1,\alpha)\)

\(\zeta_{\alpha} = \varphi(2,\alpha)\)

\(\eta_{\alpha} = \varphi(3,\alpha)\)

and what comes after eta? It's theta! Therefore:

\(\theta_{\alpha} = \varphi(4,\alpha)\)

And we can keep going on:

\(\iota_{\alpha} = \varphi(5,\alpha)\)

\(\kappa_{\alpha} = \varphi(6,\alpha)\)

\(\lambda_{\alpha} = \varphi(7,\alpha)\)

\(\mu_{\alpha} = \varphi(8,\alpha)\)

\(\nu_{\alpha} = \varphi(9,\alpha)\)

\(\xi_{\alpha} = \varphi(10,\alpha)\)

\(\omicron_{\alpha} = \varphi(11,\alpha)\)

\(\pi_{\alpha} = \varphi(12,\alpha)\)

\(\rho_{\alpha} = \varphi(13,\alpha)\)

\(\sigma_{\alpha} = \varphi(14,\alpha)\)

\(\tau_{\alpha} = \varphi(15,\alpha)\)

\(\upsilon_{\alpha} = \varphi(16,\alpha)\)

\(\phi_{\alpha} = \varphi(17,\alpha)\)

\(\chi_{\alpha} = \varphi(18,\alpha)\)

\(\psi_{\alpha} = \varphi(19,\alpha)\)

\(\omega_{\alpha} = \varphi(20,\alpha)\)

,which indicates:

\( \omega_1 = \varphi(20,1) < \Omega \)

Happy April Fools.