I need something like this, a collection of elements which contains no duplicates of any element. Does Common Lisp, specifically SBCL, have any thing like this?
Yes, it has sets. See this section on "Sets" from Practical Common Lisp.
Basically, you can create a set with pushnew and adjoin, query it with member, member-if and member-if-not, and combine it with other sets with functions like intersection, union, set-difference, set-exclusive-or and subsetp.