Let $\mathcal {S}$ denote the class of orthomodular posets in which all maximal Frink ideals are selective. Let $\mathcal {R}$ (resp. HCode $\mathcal {T}$ ) be the class of orthomodular posets defined by the validity of the following implications: $P\in \mathcal {R}$ if the implication a,b ∈ P, $a\wedge b=0\ \Rightarrow \ a\le b^{\prime }$ holds (resp., $P\in \mathcal {T}$ if the implication $a\wedge b=a\wedge b^{\prime }=0\ \Rightarrow \ a=0$ holds). In this note we prove the following slightly surprising result: $\mathcal {R}\subset \mathcal {S}\subset \mathcal {T}$ . Since orthomodular posets are often understood as quantum logics, the result might have certain bearing on quantum axiomatics.

中文翻译：

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论正交调式中的 Frink 理想

让 $\mathcal {S}$ 表示所有最大 Frink 理想都是选择性的正模偏序组。令 $\mathcal {R}$ (resp. HCode $\mathcal {T}$ ) 是由以下蕴涵的有效性定义的正模偏序组： $P\in \mathcal {R}$ 如果蕴涵 a， b ∈ P, $a\wedge b=0\ \Rightarrow \ a\le b^{\prime }$ 成立（相应地，$P\in \mathcal {T}$ 如果蕴涵 $a\wedge b=a \wedge b^{\prime }=0\ \Rightarrow \ a=0$ 成立）。在本笔记中，我们证明了以下稍微令人惊讶的结果： $\mathcal {R}\subset \mathcal {S}\subset \mathcal {T}$ 。由于正模偏序集通常被理解为量子逻辑，因此结果可能对量子公理有一定的影响。