The core of early Buddhism revolves around the concepts of 'dukkha , annica and anatta'
The core of early Buddhism actually revolves around the concepts of 'annica, dukkha and anatta'. That you mix up the order of these words show that you do not understand their reality because the later is perceived by perceiving the former.
Put a little simplistically...it is a primary source of misery.
Put accurately, it is the sole source of misery.
So over time the 'Anatta Doctrine' has morphed into ideas that there is no soul ... which is a teaching which can not be found in any early text.
No teaching about the existence of a 'soul', in the Indian meaning of 'atman' (rather than Christian 'conscience'), can be found in the early text.
Modern Buddhism struggles here because it does have the notion of rebirth and advocates the aim is to escape the endless cycle of rebirths [because it is suffering etc. etc.] all of which makes no logical sense and is ultimately based on a complete misunderstanding of the Buddha's original intentions.