Collocations for criterion - noun

sole
basic, main, primary (esp. AmE)
strict, stringent
objective
admission, eligibility, inclusion, selection

range, set

fit, fulfil/fulfill, meet, satisfy
She failed to meet the stringent selection criteria.

define, develop, establish, lay down (BrE), lay out (AmE), set
adopt, apply, use
The other groups agreed to adopt our criteria.

according to a/the criterion
Team members will be selected according to strict criteria.

by a/the criterion
By this criterion, very few people are suitable.

criterion for
The report lays down criteria for disciplining staff.