Zoom link:
https://huji.zoom.us/j/81946138956?pwd=vSDISONNjahicywGIWtlqTSpKwZjfW.1
Meeting ID: 819 4613 8956
Passcode: 055973
Title: Universal wide Aronszajn line
Abstract: Given a regular cardinal κ, a κ-Aronszajn tree is a tree of
size κ where every chain
and level in the tree are of size < κ. A κ-Aronszajn line is a linear
order of size κ such
that it does not order-embed κ with both the ∈ nor the ∋ order, and does
not contain
a dense subset of size κ. The definition of a wide κ-Aronszajn tree and
the proof of the
consistency of the existence of a wide ω_2-Aronszajn tree that embeds
all other such trees
(i.e., universal) is done in [1]. We define the notion of a wide
κ-Aronszajn line. Then, we
prove the consistency of the existence of a universal wide ω_2-Aronszajn
line. This will be
done via a very similar strategy to that in [1].
[1] Omer Ben-Neria, Menachem Magidor, and Jouko Väänänen. Aronszajn
trees and maxi-
mality– part 2 (https://arxiv.org/pdf/2305.07880v1)