Our first aim is to study the ergodic properties of $T$.
Our aim here is to give some sort of “functorial” description of $K$ in terms of $G$.
This connection has been exploited to construct various infinite families, with the aim of filling possible gaps.
In the remainder of this section, we study some properties of $K$, with the eventual aim (not realized yet) of describing $K$ directly using $G$.
the broad $\langle$general/central/main/major/primary/limited/modest/underlying/original$\rangle$ aim
We aim to prove the following inequality: ......
These results therefore describe the very close connection between the method of encoding and the structures we are aiming to classify.
Aiming for a contradiction, suppose that ......