Earth-Omega
"Earth-Omega" was an incredibly advanced parallel Earth, home of the prominent scientist Kell Mossa. Like the Maltusian Krona, Mossa wished to see the beginning of the universe; however, he linked the matter multiverse and Anti-Matter Universe together in order to do so. His experiment unleashed enough energy to reawaken the Anti-Monitor, whose first action was to obliterate Earth-Omega's universe with a wave of anti-matter. Learning that doing so gave him great power (and drained that of the Monitor), the Anti-Monitor set upon his course of multiversal destruction. Mossa was able to survive due to his presence in the viewing device, and he was transformed into the Pariah by the Monitor to help in the battles to come.
Post-Crisis
Post-Crisis, "Earth-Omega" was an alternate dimension, not an alternate Earth.
Comments
The designation "Earth-Omega" was coined by Jonathan Woodward of the Annotated Crisis site.