Logopolis

Logopolis was a planet of mathematicians, the Logopolitans, who utilized Block Transfer Computations, with the Monitor as their representative.

The Doctor had visited it while traveling with Steven and Dodo. (DWU: He Jests at Scars...) The Doctor visited again to ask the Logopolitans to help restore the chameleon circuit of his TARDIS. Sometime earlier, the Logopolitans had set up an exact reply of the Pharos Project dish in order to send Block Transfer Computations out into the universe to maintain the existence of the CVEs which, by removing entropy from our universe, enabled it to keep on surviving.

The Watcher also arrived there at the same time as the Doctor with Nyssa, whom the Doctor and Adric had last met on Traken.

The arrival of the Master fatally disrupted life there and he killed Logopolitans at random with his Tissue Compression Eliminator. Eventually, because their Block Transfer Computations no longer worked, the planet itself began to crumble and lose coherence, as did the inhabitants, including the Monitor. (DW: Logopolis)

If the Valeyard had defeated the Doctor and become the Doctor, he would then accidentally destroy his fourth incarnation on his way to Logopolis and would need to go back through time to destroy Logopolis so that the Fourth Doctor would not think to go there, therefore not being destroyed by the Valeyard. But during this second attempt, he destroyed his first incarnation while he was on Logopolis, making his existence unstable. (DWU: He Jests at Scars...)