Well acquisition of power through military means was a Roman tradition since Sullas march on Rome in 88 BCE though, so technically they have just as much of a claim as Charlemagne, the HRE, and the Tzars. A better one even since they actually conquered “new Rome” and its people and held it. What matters though is that they did claim the title of Caesar just as the other self-proclaimed successors of Rome did.
The Byzantine Empire didn’t turn into the Ottoman Empire, it was conquered by them.
Well acquisition of power through military means was a Roman tradition since Sullas march on Rome in 88 BCE though, so technically they have just as much of a claim as Charlemagne, the HRE, and the Tzars. A better one even since they actually conquered “new Rome” and its people and held it. What matters though is that they did claim the title of Caesar just as the other self-proclaimed successors of Rome did.