Well, you can always use an element reference (ISO/IEC 9075-2:1999, 6.13 ):
WHERE QUALIFICATION(1) = 'BSC'
OR QUALIFICATION(2) = 'BSC'
...
Of course, the problem is that you need to write a comparison for each possible position.
I am not aware of any operators that allows you to compare a scalar with an array, although I would suppose a DBMS that has native support for ARRAY types ould let you create a function that does the job.
I must say I never had the need for array types - I would typically build a one-to-many detail table, or in rare cases, add multiple columns (yeah - a repeating group. send the relational police to hunt me if you like :)
Would you care to explain why you need to know this, or what problem you are trying to solve with an ARRAY?