For starters, the ul > ul selector will not work, since ul elements may not be direct children of other ul elements. You need to use ul > li > ul in this case.
What you can do for target depth levels is root for the first parent of the ul element. For example, if your top level ul was a direct child of the body element, you can simply add body > to your selectors:
body > ul, /* Level 1 */ body > ul > li > ul, /* Level 2 */ body > ul > li > ul > li > ul { } /* Level 3 */
For what's worth it, but with the right specificity, a single ul selector would be enough to apply style to all your ul elements (unless you just want to target certain depth levels).
An autonomous selector for the target depth, unfortunately, does not exist. You may be approaching this incorrectly, but why don't you add the class or id attribute to the specific ul you want to use and use instead as a selector?
James donnelly
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