Returns that do not meet the necessary criteria are sent back to the taxpayers.

Thus, AP is a necessary but insufficient criterion for free will.

He did not note however, that temporality is the only necessary criterion among those aspects.

The first two constructs point to imagination as a necessary criterion for empathy to occur.

How does that fit in with the necessary criteria for claiming a government funded arts project?

In this approach, theories are a specific category of models which fulfill the necessary criteria.

For best results, fill in as few criteria as necessary.

This is in the line of "necessary but not sufficient criteria" of course.

The necessary criterion is an individual's well-founded, specific fear of political persecution.

Critics have said City Hall has not made clear the criteria necessary to save a garden.