论文标题
连续性假设和可溶性公理在经济理论和数学心理学中：个人选择理论的巩固
Continuity Postulates and Solvability Axioms in Economic Theory and in Mathematical Psychology: A Consolidation of the Theory of Individual Choice
论文作者
论文摘要
本文介绍了四个定理，这些定理将数学经济学中的连续性假设与数学心理学中的公理相关，并将它们在替代补充假设下进行排名。定理1将连续性概念（完整，独立，wold，弱，Archimedean，混合物）与在二进制关系的完整性和传递性下的溶解度（受限，无限制）联系起来。定理2使用单独连续函数的原始概念来回答当关系上的类似属性完全连续时。定理3提供了portmanteau定理，涉及限制可溶解性与弱单调性下的各种连续性概念之间的等效性。最后，定理4提出了定理3的变体，该变体遵循定理1在分配维度要求并提供求解性和连续性概念之间的部分等价方面。这些定理是出于其在表示定理中的潜在使用而动机。
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.
