An order isomorphism is a bijection preserving and reflecting the order relation. It transfers well-foundedness and order type between a coded order and its ordinal interpretation.
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Order isomorphism is a concept from order theory, which is a branch of mathematics dealing with the study of ordered sets. Two ordered sets (or posets) are said to be order isomorphic if there exists a bijection (a one-to-one and onto function) between the two sets that preserves the order relations. More formally, let \( (A, \leq_A) \) and \( (B, \leq_B) \) be two ordered sets.