Lorenz Halbeisen - Four Cardinals and Their Relations in ZF

This talk was part of the Workshop on "Set-Theory" held at the ESI July 4 to 8, 2022.

For a set M, fin(M) denotes the set of all finite subsets of M, M^2 denotes the Cartesian product MxM, [M]^2 denotes the set of all 2-element subsets of M and seq(M) denotes the set of all finite sequences without repetition which can be formed with elements of M. Furthermore, for a set S, let |S| denote the cardinality of S. Under the assumption that the four cardinalities |[M]^2|, |M^2|, |fin(M)|, |seq(M)| are pairwise distinct and pairwise comparable in ZF, there are six possible linear orderings between these four cardinalities. We show that at least five of the six possible linear orderings are consistent with ZF.

Видео Lorenz Halbeisen - Four Cardinals and Their Relations in ZF канала Erwin Schrödinger International Institute for Mathematics and Physics (ESI)