Club Chang's Conjecture
release_tmkvhdxpcrhw5nzukqr25lg2yy
by
Sean Cox, Saharon Shelah
2019
Abstract
Chang's Conjecture (CC) asserts that for every F:[ω_2]^<ω→ω_2, there exists an X that is closed under F such that
|X|=ω_1 and |X ∩ω_1| =ω. By classic results of Silver
and Donder, CC is equiconsistent with an ω_1-Erdos cardinal. Using
stronger large cardinal assumptions (between o(κ) = κ^+ and
o(κ) = κ^++), we prove that it is consistent to also require that
X contains a closed unbounded set of ordinals in sup(X ∩ω_2). We denote this stronger principle Club-CC, and also show
that, unlike CC, Club-CC implies failure of certain weak square principles.
In text/plain
format
Archived Content
There are no accessible files associated with this release. You could check other releases for this work for an accessible version.
Know of a fulltext copy of on the public web? Submit a URL and we will archive it
1809.09280v4
access all versions, variants, and formats of this works (eg, pre-prints)