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drizzy
drizzy
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cofinality of $(P(\kappa)/NS,\subseteq)$

Let $\kappa$ be a cardinal (I'm most interested in $\kappa=\aleph_{\omega+1}$ but I suspect a general answer is known). What is the cofinality of $(P(\kappa),\subseteq)$$(P(\kappa)/NS,\subseteq)$? By this I mean the least cardinal $\lambda$ such that there exists a subcollection $X\subseteq P(\kappa)$$X\subseteq P(\kappa)/NS$ of size $\lambda$ such that for any $A\in P(\kappa)$ there is $B\in X$ with $A\subseteq B$.

Here we consider $P(\kappa)/NS$ to be without the largest element.

This may be trivial but it's been bugging me all day!

Drake

cofinality of $(P(\kappa),\subseteq)$

Let $\kappa$ be a cardinal (I'm most interested in $\kappa=\aleph_{\omega+1}$ but I suspect a general answer is known). What is the cofinality of $(P(\kappa),\subseteq)$? By this I mean the least cardinal $\lambda$ such that there exists a subcollection $X\subseteq P(\kappa)$ of size $\lambda$ such that for any $A\in P(\kappa)$ there is $B\in X$ with $A\subseteq B$.

This may be trivial but it's been bugging me all day!

Drake

cofinality of $(P(\kappa)/NS,\subseteq)$

Let $\kappa$ be a cardinal (I'm most interested in $\kappa=\aleph_{\omega+1}$ but I suspect a general answer is known). What is the cofinality of $(P(\kappa)/NS,\subseteq)$? By this I mean the least cardinal $\lambda$ such that there exists a subcollection $X\subseteq P(\kappa)/NS$ of size $\lambda$ such that for any $A\in P(\kappa)$ there is $B\in X$ with $A\subseteq B$.

Here we consider $P(\kappa)/NS$ to be without the largest element.

This may be trivial but it's been bugging me all day!

Drake

Source Link
drizzy
drizzy
  • 115
  • 5

cofinality of $(P(\kappa),\subseteq)$

Let $\kappa$ be a cardinal (I'm most interested in $\kappa=\aleph_{\omega+1}$ but I suspect a general answer is known). What is the cofinality of $(P(\kappa),\subseteq)$? By this I mean the least cardinal $\lambda$ such that there exists a subcollection $X\subseteq P(\kappa)$ of size $\lambda$ such that for any $A\in P(\kappa)$ there is $B\in X$ with $A\subseteq B$.

This may be trivial but it's been bugging me all day!

Drake