User blog comment:DontDrinkH20/Some Explanations of Certain Large Cardinals/@comment-35870936-20181017021650/@comment-25601061-20181017210847

@P bot:

Ecl1psed is not referring to replacing actual large cardinals with symbols in OCFs, but rather replacing them with smaller ordinals that can still behave like their larger counterparts. This is possible: for example, instead of using regular cardinals in Buccholz's OCF, we could use admissible ordinals. In fact, one can even define an OCF such that its definition guarantees that it collapses the smallest possible ordinal that behaves like we need it to - I like to call these types of OCFs minimal collapse OCFs.