11,582
pages

Since the comparison (or even the well-definedness) of the numbers in this level is unknown, the order of entries does not necessarily imply the order of the sizes (note that BEAF numbers beyond tetrational arrays, which are ill-defined, should not lie in this level, see also Category:Class disputed and Talk:Meameamealokkapoowa oompa#Size issue). Also, several numbers are defined by an OCF, which is uncomputable, and are not known to be computable, particularly beyond $$\psi_0(\Phi_1(0))$$ level on the fast-growing hierarchy with respect to the system of fundamental sequences for Extended Buchholz's function, where $$\psi$$ is Extended Buchholz's function and $$\Phi_1(0)$$ is the least omega fixed point. Moreover, several approximations are using unspecified (or even ill-defined) OCFs, and hence might be mathematically meaningless. Note that various systems of fundamental sequences are used for comparisons on this level.

## $$f_{\psi_0(\Omega_\omega)}^2(10)$$ ~ $$f_{\psi_0(\Phi_1(0))+1}(10)$$

• Pair sequence number, $$\approx f_{\psi(\Omega_\omega)+1}(10)$$
• 段階配列数, $$\approx f_{\psi(\Omega_{\omega})+1}(100)$$
• Big boowa, {3,3,3 / 2}
• Great big boowa, {3,3,4 / 2}
• Grand boowa, {3,3,big boowa / 2} = {3,2,2,2 / 2}
• Gigantic big boowa, {3, 3, {3, 3, 4 / 2} / 2} = {3, 3, great big boowa / 2}
• Gorged boowa, {3, 3, {3, 3, {3, 3, 3 / 2} / 2} / 2} = {3, 3, grand boowa / 2}
• Gulp big boowa, {3, 3, {3, 3, {3, 3, 4 / 2} / 2} / 2} = {3, 3, gigantic big boowa / 2}
• Super gongulus, {10,10 (100) 2 / 2}
• Wompogulus, {10,10 (10) 2 / 100}
• Guapamonga, 10100 && (10100 & 10)
• Guapamongaplex, 10guapamonga && (10guapamonga & 10)
• Big Chunk, {10,100 [1 [1 [1 \2,2 3] 2] 2] 2}
• Bimixommwil, $$f_{\psi(\Omega_{\psi(\Omega)})}(10)$$
• Trimixommwil, $$f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})}(10)$$
• Quadrimixommwil, $$f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})}(10)$$
• Quintimixommwil, $$f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})})}(10)$$
• Sextimixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{6\ \Omega's}}(10)$$
• Septimixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{7\ \Omega's}}(10)$$
• Octimixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{8\ \Omega's}}(10)$$
• Nonimixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{9\ \Omega's}}(10)$$
• Dekomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10\ \Omega's}}(10)$$
• Binommwil, $$f_{\psi(\Omega_\Omega)}(10)$$
• Hektomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{100\ \Omega's}}(10)$$
• Kilomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{1000\ \Omega's}}(10)$$
• Megomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^6\ \Omega's}}(10)$$
• Gigomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^9\ \Omega's}}(10)$$
• Teromixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{12}\ \Omega's}}(10)$$
• Petomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{15}\ \Omega's}}(10)$$
• Exomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{18}\ \Omega's}}(10)$$
• Zettomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{21}\ \Omega's}}(10)$$
• Yottomixommwil, $$f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{24}\ \Omega's}}(10)$$
• Nucleatrixul, 200![[[200200]200]200]
• Trinommwil, $$f_{\psi(\Omega_{\Omega_\Omega})}(10)$$
• Nucleaquaxul, 200![[[[200200]200]200]200]
• Quadrinommwil, $$f_{\psi(\Omega_{\Omega_{\Omega_\Omega}})}(10)$$
• Quintinommwil, $$f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_\Omega}}})}(10)$$
• Sextinommwil, $$f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_{\Omega_\Omega}}}})}(10)$$
• Septinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{7\ \Omega's})}(10)$$
• Octinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{8\ \Omega's})}(10)$$
• Noninommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{9\ \Omega's})}(10)$$
• Dekinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10\ \Omega's})}(10)$$
• Hektinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{100\ \Omega's})}(10)$$
• Big hoss, $$\lbrace 100,100 \underbrace{///\cdots ///}_{100} 2\rbrace$$
• Grand hoss, $$\lbrace 100,100 \underbrace{///\cdots ///}_{100} 100\rbrace$$
• Kilinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{1000\ \Omega's})}(10)$$
• Meginommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^6\ \Omega's})}(10)$$
• Giginommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^9\ \Omega's})}(10)$$
• Terinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{12}\ \Omega's})}(10)$$
• Petinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{15}\ \Omega's})}(10)$$
• Exinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{18}\ \Omega's})}(10)$$
• Zettinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{21}\ \Omega's})}(10)$$
• Yottinommwil, $$f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{24}\ \Omega's})}(10)$$
• Great big hoss, $$\lbrace \text{big hoss},\text{big hoss} \underbrace{///\cdots ///}_{\text{big hoss}} 2\rbrace$$

## $$f_{\psi_0(\Phi_1(0))+1}(10)$$ ~

Some of these numbers are based on functions which are neither provable nor disprovable to be total in $$\mathrm{ZFC}$$.

## Stronger set theory level

These numbers are based on functions which are not provably total in $$\mathrm{ZFC}$$, but based on functions that are known to be provably total in stronger set theories.