Patterns of resemblance
The patterns of resemblance (PoR) are a system of ordinal-notations introduced by TJ Carlson. It is superficially similar to stability, yet is a notation for recursive rather than nonrecursive ordinals, and uses elementary substructures between ordinals themselves, instead of between ranks of the constructible universe. It uses a structure also found in BMS known as respecting forests, and was originally believed to have the same limit as BMS.