It is proclaimed that there is no continuity between the ancient and modern Greeks, not even with those of the Byzantine Empire. Thus, the theory of Fallmerayer is revived in various scientific ways.
It was admittedly difficult for there to be a continuous and stable presence of Greeks under conditions of subjugation and slavery. However, the Greek world is a continuous and dynamic presence and often prevails over the "wild conqueror" (ferum victorem), as Horace says. The Greek element managed to overcome even extreme Christian reactions and give universal permeability to Christianity. Imposing your spiritual and linguistic culture on the one who officially dominates from within is the most irrefutable testimony of Greek continuity.
They also claim that every trace of Greekness was lost in the sea of population elements that flooded the Greek territory as invaders. The presence of such and other peoples in the Greek territory is undeniable. However, what escaped Fallmerayer and his present-day followers is this very important fact: no such people became the ruling power. On the contrary, over time, the Greek world assimilated foreign elements.