Finitist set theory

as classical finitists, and those who do not allow potentially infinite objects as strict finitists: for example, a classical finitist would allow statements

urelements the objects of any theory or of the physical universe. In finitist set theory, urelements are mapped to the lowest-level components of the target

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains

sets. This is the Fall and original sin of [Cantor's] set theory The difficulty with finitism is to develop foundations of mathematics using finitist

and in particular that the natural numbers form an infinite set. However, some finitist philosophers of mathematics and constructivists still object