Original sentence: The term "Catholic Church" is freely used within this article without suggesting acceptance of any claims implicit in that term, while "Roman Catholic Church" is used without endorsing the view that this Church is merely part of some larger "Catholic Church"; both terms are used here as alternative names for the entire Church which claims to be "governed by the successor of Peter and by the bishops in communion with him," without endorsing that claim
Edited sentence: The term "Catholic Church" is freely used within this article without suggesting acceptance of any claims implicit in that term, while "Roman Catholic Church" is used without endorsing the view that this Church is merely part of some larger "Catholic Church"; both terms are used here as alternative names for the entire Church "which is governed by the successor of Peter and by the bishops in communion with him