When Eye of Singularity enters, destroy each permanent with the same name as another permanent, except for basic lands. They can't be regenerated.
Whenever a permanent other than a basic land enters, destroy all other permanents with that name. They can't be regenerated.
This has the supertype world. When a world permanent enters, any world permanents that were already on the battlefield are put into their owners' graveyards. This is a state-based action called the "world rule." The new world permanent stays on the battlefield. If two world permanents enter at the same time, they're both put into their owners' graveyards.