In certain constructivist and predicativist frameworks, the inference from order-isomorphism to bijection requires impredicative comprehension axioms that cannot be assumed without circularity.

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Bijection(in set theory and mathematics): A perfect one-to-one matching between two sets, where every element in one set pairs with exactly one element in the other, and nothing is left unpaired.
Circularity (in logic)(as used in logic and epistemology): When a definition or argument uses itself as part of its own explanation, making it logically problematic because you can't use something to prove itself.
Impredicative comprehension axioms(as used in logic and set theory): Rules that allow mathematicians to define a set by referring to all sets (including the set being defined), which can create circular or questionable reasoning.
Order-isomorphism(as used in mathematics and logic): When two collections have the exact same structure or pattern of ordering—like how a list numbered 1,2,3 has the same structure as A,B,C.

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