Htykuut

I have not previously seen anything online that dives deeply into On:

In Conway's notation On denotes the ordinal numbers (and No denotes the set of all surreal Numbers). Basically the elements of On are just von Neumann ordinals. -Source

I would appreciate feedback on the following attempt to write large countable ordinals (& the functions that generate them) in Conway notation (my primary source of information in creating these constructions was Large Countable Ordinals):

epsilon-nought
$$varepsilon_{0}={omega,omega^omega,omega^{omega^omega},...|}$$
veblen function
$$phi={omega,varepsilon_0,zeta_{alpha},...|}$$
veblen hierarchy
$$phi_{gamma}(alpha)={phi_{0}(alpha)=omega^{alpha}, phi_{1}(alpha)=varepsilon_{alpha}, phi_{2}(alpha)=zeta_{alpha}...|}$$
feferman-schutte ordinal
$$Gamma_0=phi_{Gamma_0}(0)={phi_0(0),phi_{phi_0(0)}(0),phi_{phi_{phi_0(0)}(0)}(0),...|}$$
small veblen ordinal
$$SVO={phi_1(0), phi_{1,0}(0), phi_{1,0,0}(0),...|}$$
large veblen ordinal
$$LVO=psi(Omega^{Omega^Omega})={[???]...|}$$
bachmann-howard ordinal
$$BHO=psi(varepsilon_{Omega+1})={psi(Omega),psi(Omega^Omega),psi(Omega^{Omega^Omega})|}$$

Additionally, any online resources related to On would be greatly appreciated.