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Monroe Eskew
Monroe Eskew
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Consider the partial order $(P(\omega),\subseteq)$. Let $L$ be a dense linear suborder. Does $L$ have a countable dense subset?

(Note that it contains a copy of $\mathbb R$, via Dedekind cuts of $\mathbb Q$.)

Consider the partial order $(P(\omega),\subseteq)$. Let $L$ be a dense linear suborder. Does $L$ have a countable dense subset?

Consider the partial order $(P(\omega),\subseteq)$. Let $L$ be a dense linear suborder. Does $L$ have a countable dense subset?

(Note that it contains a copy of $\mathbb R$, via Dedekind cuts of $\mathbb Q$.)

Source Link
Monroe Eskew
Monroe Eskew
  • 18.7k
  • 5
  • 53
  • 115

Linear suborders of $(P(\omega),\subseteq)$

Consider the partial order $(P(\omega),\subseteq)$. Let $L$ be a dense linear suborder. Does $L$ have a countable dense subset?