  We show that many large cardinal notions up to measurability can be
characterized through the existence of certain filters for small models of set
theory. This correspondence will allow us to obtain a canonical way in which to
assign ideals to many large cardinal notions. This assignment coincides with
classical large cardinal ideals whenever such ideals had been defined before.
Moreover, in many important cases, relations between these ideals reflect the
ordering of the corresponding large cardinal properties both under direct
implication and consistency strength.
