[see also: desire, end, object, objective, task, purpose, intention]

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


[to do sth, at sth, for sth; see also: design, intend]

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 ......

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