经济理论与数理心理学中的连续性假设与可解性公理：个人选择理论的整合
Continuity Postulates and Solvability Axioms in Economic Theory and in Mathematical Psychology: A Consolidation of the Theory of Individual Choice
摘要：
本文提出了四个定理，数学经济学中的连续性假设连接到数学心理学中的可解性公理，并在替代补充假设下排列它们。定理1连接概念的连续性（完全，分离，沃尔德，弱沃尔德，阿基米德，混合物）与可解性（限制，无限制）下的完整性和传递性的二元关系。定理2使用分离连续函数的原始概念来回答关系上的类似性质何时是完全连续的问题。定理3给出了弱单调条件下限制可解性与各种连续性概念之间等价性的一个组合定理。最后，定理4给出了定理3的一个变体，它遵循定理1，免除了维数要求，并提供了可解性和连续性概念之间的部分等价性。这些定理的动机，他们的潜在用途表示定理。
英文摘要：
This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately-continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem 3 provides a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems.
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