Which is correct?
- The set is empty and is ordered.
- The set is empty and ordered.
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Both are equally grammatical and mean the same thing. The latter is ellipsis of the former. Which in turn is ellipsis of "The set is empty and the set is ordered".
These statements are illogical
The following is also illogical
Because, if a set is empty, there would be nothing to order or sort.
Mathematics say that the logical way to say it is
You can have a frame defined to contain ordered list of things, and such a frame could be empty.
Further illustration of the logic. Compare
This is when the differences between a participle and a gerund is crucial: Gerund ending in -ings?