Andrés Caicedo

Andrés Caicedo is the mathematician specializing in set theory identified as Andrés Eduardo Caicedo on his author homepage.^[ref] His published teaching notes develop infinite partition relations, including omega-Jónsson functions and their relationship to colourings of countably infinite subsets.^[ref]

For an infinite set $X$, an omega-Jónsson function has the form $f:[X{]}^{{\aleph }_0}\to X$, and every $Y\subseteq X$ with $|Y|=|X|$ satisfies $f([Y{]}^{{\aleph }_0})=X$. Thus a large restriction still produces every colour. His notes present a proof of existence assuming the axiom of choice, explicitly attributing the theorem and the simplified proof to their discoverers. This is a concrete example of the interaction between cardinal arithmetic and infinite combinatorics.