List of ordinal notations

This is a list of ordinal notations, arranged roughly by their strength in increasing order.


 * Unary, binary, decimal etc. (limit: \(\omega\))
 * Linear array notation separators (limit: \(\omega^\omega\))
 * Nested array notation separators (limit: \(\varepsilon_0\))
 * Primitive sequence system (limit: \(\varepsilon_0\))
 * Iterated Cantor normal form (limit: \(\varepsilon_0\))
 * Large primitive sequence system (limit: \(\varphi(\omega, 0)\))
 * Binary veblen function (limit: \(\Gamma_0\))
 * Finitary veblen function (limit: \(\psi_0(\Omega^{\Omega^\omega})\)) (this and the below OCFs are Buchholz's function until specified)
 * Schutte Klammersymbolen (limit \(\psi_0(\Omega^{\Omega^\Omega})\))
 * Pair sequence system (limit \(\psi_0(\Omega_\omega)\))
 * Ordinal notation associated to Buchholz's function (limit \(\psi_0(\Omega_{\omega + 1})\)) (this and the below OCFs are Extended Buchholz's function until specified)
 * Bird's array notation separators (limit \(\psi_0(\Omega_\Omega)\)
 * Ordinal notation associated to Extended Buchholz's function (limit \(\psi_0(\Omega_{\Omega_{\Omega_{...}}})\))
 * Address notation (limit \(\psi_0(\Omega_{\Omega_{\Omega_{...}}})\))
 * Ordinal notation associated with Rathjen's \(\psi\) function based on the least weakly Mahlo cardinal (limit \(\psi_{\chi_0(0)}(\psi_{\chi_{\varepsilon_{M+1}}(0)}(0))\) in Rathjen's \(\psi\))
 * Primary dropping array notation separators (limit (0,0,0)(1,1,1)(2,2,0) in BMS)
 * Dropping array notation separators (limit (0,0,0)(1,1,1)(2,2,1)(3,0,0) in BMS)
 * Lumi's large pair sequence system (limit (0,0,0)(1,1,1)(2,2,2) in BMS)
 * Trio sequence system (limit (0,0,0,0)(1,1,1,1) in BMS)
 * Bashicu matrix system
 * Aarex's superstrong array notation
 * Y sequence
 * \(\omega\)-Y sequence