 The motivation of putative axioms that go beyond ZFC constitutes a third concern of the philosophy of set theory (Maddy 1988; Martin 1998). One such class of principles is constituted by the large cardinal axioms. Nowadays, large cardinal hypotheses are really taken to mean some kind of embedding properties between the set theoretic universe and inner models of set theory (Kanamori 2009). Most of the time, large cardinal principles entail the existence of sets that are larger than any sets which can be guaranteed by ZFC to exist.