Let $\kappa>\omega$ be a cardinal. We say that ${\cal A}\subseteq{\cal P}(\kappa)$ is an almost disjoint family if $|A|=\kappa$ for $A\in{\cal A}$, and $|A\cap B|<\aleph_0$ for $A\neq B\in{\cal A}$. Zorn's Lemma implies that every almost disjoint family is contained in a maximal such family, whic...
I'm sorry if I'm posting this in the wrong forum. My background is in biology and medicine. I am looking to re-learn undergraduate-level mathematics, in particular discrete mathematics, calculus, and linear algebra. I did do these courses back in college, but I've since forgotten most of this. Do...
Let $\kappa>\omega$ be a cardinal. We say that ${\cal A}\subseteq{\cal P}(\kappa)$ has the finite intersection property (FIP) if $|A|=\kappa$ for $A\in{\cal A}$, and $|A\cap B|<\aleph_0$ for $A\neq B\in{\cal A}$. For which cardinals $\kappa>\omega$ is there a family with FIP ${\cal A}\subseteq {\...
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