35 research outputs found
Set Theory
This workshop included selected talks on pure set theory and its applications, simultaneously showing diversity and coherence of the subject
The set-theoretic multiverse
The multiverse view in set theory, introduced and argued for in this article,
is the view that there are many distinct concepts of set, each instantiated in
a corresponding set-theoretic universe. The universe view, in contrast, asserts
that there is an absolute background set concept, with a corresponding absolute
set-theoretic universe in which every set-theoretic question has a definite
answer. The multiverse position, I argue, explains our experience with the
enormous diversity of set-theoretic possibilities, a phenomenon that challenges
the universe view. In particular, I argue that the continuum hypothesis is
settled on the multiverse view by our extensive knowledge about how it behaves
in the multiverse, and as a result it can no longer be settled in the manner
formerly hoped for.Comment: 35 page