Full Idea
The 'ancestral' of a relation is that relation which holds when there is an indefinitely long chain of things having the initial relation.
Gist of Idea
The 'ancestral' of a relation is a new relation which creates a long chain of the original relation
Source
Peter Smith (Intro to Gödel's Theorems [2007], 23.5)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.209
A Reaction
The standard example is spotting the relation 'ancestor' from the receding relation 'parent'. This is a sort of abstraction derived from a relation which is not equivalent (parenthood being transitive but not reflexive). The idea originated with Frege.