高维广义拟序
Higher-dimensional generalized quasiorders
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中文总结 AI 辅助
本文证明克隆对固定元数d满足类似一元决定性质当且仅当由d维高维广义拟序决定，并定义了相应的高维自反性与传递性。
中文摘要 AI 辅助
众所周知，拟序的多态克隆由其一元部分决定，即任何运算若满足以下条件：将其某些变量固定为常数值后得到的所有一元函数都是多态，则该运算是多态。我们证明，一个克隆对特定固定元数 $d$ 满足类似性质，当且仅当它由一组我们称之为维数等于 $d$ 的高维广义拟序所决定。我们定义了高维广义拟序，并将自反性和传递性适当推广到高维情形，这些推广依赖于对“矩形”元数的显式分析。
英文摘要
It is well known that the polymorphism clone of a quasiorder is determined by its unary part, in the sense that any operation is a polymorphism if it satisfies the condition that all unary functions obtained by fixing some of its variables at constant values are polymorphisms. We show that a clone satisfies an analogous property for a particular fixed arity $d$ if and only if it is determined by a collection of what we call higher-dimensional generalized quasiorders whose dimension is equal to $d$. We define higher-dimensional generalized quasiorders with the appropriate generalizations of reflexivity and transitivity to the higher-dimensional setting, which rely on an explicit analysis of 'rectangular' arity.
发表机构
- TU Dresden（德累斯顿工业大学）
机构由 AI 辅助整理，请以论文原文为准。
