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Are FIDE World Champions after the 1993 Kasparov-Short match, i.e. Khalifman, Ponomariov, Kasymdžanov, Topalov, (not counting Karpov and Anand, for obvious reasons) to be considered actual World Champions, or not? I think that the real World Champions after Kasparov are Kramnik (who beat Kasparov), then Anand, and of course Carlsen. What's the chess world's view on this?

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    Most people call them FIDE world champions, as opposed to "Chess World Champions." It's meant to be a sort of asterick to the title of "world champion." Commented Oct 22, 2018 at 23:12
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    The only tough one is Topalov, because he was clearly the strongest player for a while and won the title against the strongest players in world in a round robin. Commented Oct 25, 2018 at 8:44

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The answer is that both the FIDE world champions and the PCA world champions were world champions.

The situation was actually less chaotic than the normal situation in boxing. In boxing there are four bodies awarding world champion titles. They are -

  • WBA - World Boxing Association
  • WBC - World Boxing Council
  • IBF - International Boxing Federation
  • WBO - World Boxing Organization

In the heavyweight division the British fighter, Anthony Joshua, holds three of the four titles (WBA, IBF, WBO) but in the light heavyweight division four different boxers hold the four titles -

  • WBA - Dmitry Bivol
  • WBC - Oleksandr Gvozdyk
  • IBF - Artur Beterbiev
  • WBO - Sergey Kovalev

If boxers are clever enough to get their heads round having up to four different world champions in one weight division then I'm sure chess players are clever enough to manage just two for the short period of time of the existence of the PCA.

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