5
$\begingroup$

I've been making my way through the new Kunen and I've come across an exercise that I can't work out. The question is this:

Let $\kappa$ be a singular cardinal. Show that there is a collection $A$ of $\kappa$ many two-element subsets of $\kappa$ such that no element of $[A]^\kappa$ forms a $\Delta-$ system. Where $[A]^\kappa$ is the set of subsets of A of size $\kappa$.

Any help would be appreciated (i.e. hints welcome).

  • 1
    What is $A$ in this context?2012-10-19
  • 0
    @AsafKaragila From context I presume it refers to the (otherwise unnamed) collection of two-element subsets of $\kappa$; I've edited the post slightly to reflect that. cody, if my edits are incorrect, please feel free to revert.2012-10-19

1 Answers 1