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Monroe Eskew
Monroe Eskew
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Definition: Let $B$ be a boolean algebra. Say $X \subseteq B$ is quasi-dense in $B$ if for all $b \in B$, there is $x \in X \setminus$ { $0,1$ } such that either $x \leq b$ or $b \leq x$.

Question: Suppose $A \subseteq B \subseteq C$ are atomless boolean algebras, $A$ is quasi-dense in $B$, and $B$ is densedense in $C$. Does it follow that $A$ is quasi-dense in $C$?

Definition: Let $B$ be a boolean algebra. Say $X \subseteq B$ is quasi-dense in $B$ if for all $b \in B$, there is $x \in X \setminus$ { $0,1$ } such that either $x \leq b$ or $b \leq x$.

Question: Suppose $A \subseteq B \subseteq C$ are boolean algebras, $A$ is quasi-dense in $B$, and $B$ is dense in $C$. Does it follow that $A$ is quasi-dense in $C$?

Definition: Let $B$ be a boolean algebra. Say $X \subseteq B$ is quasi-dense in $B$ if for all $b \in B$, there is $x \in X \setminus$ { $0,1$ } such that either $x \leq b$ or $b \leq x$.

Question: Suppose $A \subseteq B \subseteq C$ are atomless boolean algebras, $A$ is quasi-dense in $B$, and $B$ is dense in $C$. Does it follow that $A$ is quasi-dense in $C$?

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Monroe Eskew
Monroe Eskew
  • 18.6k
  • 5
  • 53
  • 115

Quasi-dense subsets of boolean algebras

Definition: Let $B$ be a boolean algebra. Say $X \subseteq B$ is quasi-dense in $B$ if for all $b \in B$, there is $x \in X \setminus$ { $0,1$ } such that either $x \leq b$ or $b \leq x$.

Question: Suppose $A \subseteq B \subseteq C$ are boolean algebras, $A$ is quasi-dense in $B$, and $B$ is dense in $C$. Does it follow that $A$ is quasi-dense in $C$?