Complex sentence: Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics, but they did not explicitly exclude the possibility of the existence of a set that belongs to itself.
Split into simpler sentences: Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics. But they did not explicitly exclude the possibility of the existence of a set that belongs to itself.