Logic Seminar
In a paper from 1980, Shelah constructed a Jonsson group of size ℵ1. Assuming CH, he moreover obtained what is now known as a
"Shelah group" of size ℵ1, i.e., a group of size ℵ1 such that for some integer N, the collection of all N-sized words over the
alphabet of any given uncountable subset of the group resurrects the whole group. In this talk, we shall present a ZFC construction of a Shelah group at the level of any successor of a regular cardinal. We shall also address the problem of constructing Shelah groups at successors of singulars and
at inaccessibles. This is a joint work with Assaf Rinot.