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Unified Representability of Total Preorders and Interval Orders through a Single Function: The Lattice Approach

机译:通过一个函数实现的总预购和间隔订单的统一可表示性:格子法

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摘要

We introduce a new approach that deals, jointly and in a unified manner, with the topics of numerical (continuous) representability of total preorders and interval orders. This setting is based on the consideration of increasing scales and the systematic use of a particular kind of codomain, that has a key lattice theoretical structure of a completely distributive lattice and allows us to use a single function (taking values in that codomain) in order to represent both kinds of binary relations.
机译:我们引入了一种新的方法,该方法以统一方式统一处理总预订单和间隔订单的数字(连续)可表示性主题。此设置是基于对规模不断增长和特定种类的共域的系统使用的考虑,该共域具有完全分布晶格的关键晶格理论结构,并允许我们按顺序使用单个函数(在该共域中取值)代表两种二进制关系。

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