Four Cardinals and Their Relations in ZF

Lorenz Halbeisen (ETH Zurich)

Jul 05. 2022, 11:00 — 11:30

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.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Set-Theory (Workshop)
Organizer(s):
Jörg Brendle (Kobe U)
Vera Fischer (U of Vienna)
Sy David Friedman (U of Vienna)