User blog:Bubby3/Guesses about the strength of BMS and the Catching Hierarchy.

Here is some warp up with the known comparisons Here are my guesses:
 * (0,0,0)(1,1,1) has level \(C(0)\)
 * (0,0,0)(1,1,1)(2,1,1)(3,1,1) has level \(C(\Omega)\)
 * (0,0,0)(1,1,1)(2,2,0) has level \(C(\varepsilon_{Omega+1})\)
 * (0,0,0)(1,1,1)(2,2,1) has level \(C(C_1(\Omega))\)
 * (0,0,0)(1,1,1)(2,2,1)(2,2,0) has level \(C(varepsilon_{C_1(\Omega)+1})\)
 * (0,0,0)(1,1,1)(2,2,1)(2,2,1) has level \(C(C_1(\Omega 2))\)
 * (0,0,0)(1,1,1)(2,2,1)(3,0,0) has level \(C(C_1(\Omega \omega))\) or the limit of DAN
 * (0,0,0)(1,1,1)(2,2,1)(3,2,1) has level \(C(C_1(\Omega ^ 2))\)
 * (0,0,0)(1,1,1)(2,2,1)(3,2,1)(4,2,1) has level \(C(C_1(\Omega ^ \Omega))\)
 * (0,0,0)(1,1,1)(2,2,1)(3,3,0) has level \(C(C_1(\varepsilon_{\Omega + 1}))\)
 * (0,0,0)(1,1,1)(2,2,1)(3,3,1) has level \(C(C_1(C_1(\Omega)))\)
 * (0,0,0)(1,1,1)(2,2,1)(3,3,1)(4,4,1) has level \(C(C_1(C_1(C_1(\Omega))))\)
 * (0,0,0)(1,1,1)(2,2,2) has level \(C(\Omega_2)\)
 * (0,0,0)(1,1,1)(2,2,2)(3,3,2) has level \(C(C_2(\Omega_2))\)
 * (0,0,0)(1,1,1)(2,2,2)(3,3,3) has level \(C(\Omega_3)\)
 * (0,0,0,0)(1,1,1,1) has level \(C(\Omega_\omega)\)