Jónsson function

Summary

In mathematical set theory, an ω-Jónsson function for a set x of ordinals is a function $f:[x]^\omega\to x$ with the property that, for any subset y of x with the same cardinality as x, the restriction of $f$ to $[y]^\omega$ is surjective on $x$. Here $[x]^\omega$ denotes the set of strictly increasing sequences of members of $x$, or equivalently the family of subsets of $x$ with order type $\omega$, using a standard notation for the family of subsets with a given order type. Jónsson functions are named for Bjarni Jónsson.