关于合理字典序构造唯一性定理的注记

A Note on the Uniqueness for the Construction of Rational Lexicographic Order

研究了构造合理字典序的唯一性条件，着重分析了以自反演序为基础的字典序构造中确定合理字典序的理性条件，提出了一组新的构造合理字典序的理性条件——广义单调性条件Ｍ＋＋和Ｈｅｉｎｅｒ－Ｐａｃｋａｒｄ理性条件Ｋ＋，构造了唯一满足这组理性条件的弱序Ｌ，推广了Ｈｅｉｎｅｒ－Ｐａｃｋａｒｄ唯一性定理．

The uniqueness condition for the construction of a rational lexicographic order is studied. Emphasis is laid on the analysis of the rational conditions for the determination of a rational lexicographic order in the order construction based on the anagrammatic reflexive signed order. A set of new rational conditions, generalized monotonicity condition M ++ and Heiner Packards condition K + , is proposed. A weak order  L is constructed to satisfy the conditions mentioned above. It has been proved that  L is the weak order which satisfies uniquely the new rational conditions. The uniqueness theorem by Heiner Packard is, therefore, generalized.