I\'m trying to create a relation where any of four different parts may be included, but any collection of the same parts should be handled as unique.
Example: An ass
This is a Feature (though not what I expected, either).
This thread suggests making your key a Primary key to get the behavior you expected:
This is a feature - a NULL value is an undefined value, therefore two NULL values are not the same. Can be a little confusing but makes sense when you think about it.
A UNIQUE index does ensure that non-NULL values are unique; you could specify that your column not accept NULL values.