Seminario - Strong Colorings

Giovedì 17 Ottobre alle ore 16:00, in aula seminari, il professor Menachem Kojman della Ben Gurion University di Be’er Sheva, Israele, terra’ un seminario dal titolo: “Strong Colorings”. Tutti sono invitati a partecipare.
Titolo: Strong Colorings
Abstract: Abstract. A strong $\mu$-coloring on a cardinal $\kappa$ is a function $f:[\kappa]^2\to \mu$ --- a coloring of undordered pairs from $\kappa$ with $\mu$ colors --- with the property that for every $A\subseteq \k$ of cardinality $\kappa$, all $\mu$ colors occur on $[A]^2$, that is, for every $\gamma<\kappa$ there are $\alpha<\beta$ in $A$ such that $f(\{\a,\b\})=\gamma$. Sierpinski construction a $2$-strong coloring on $\aleph_1$ and later strong colorings with various additional properties were constructed by Erd\H os and H\'ajnal with the GCH. Todorcevic introduced the method of "minimal walks" or "ordinal walks" and with it constructed a strong $\aleph_1$ coloring on $\aleph_1$.
We shall present a short proof of Todorcevic's coloring and discuss stronger versions of strong colorings, in particular the one defined by Shelah, following Galvin, which enables the construction of two topological spaces each of which satisfies the $\kappa^+$-chain conditions but whose product fails it.