Club Chang's Conjecture release_tmkvhdxpcrhw5nzukqr25lg2yy

by Sean Cox, Saharon Shelah

Released as a article .

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.
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Type  article
Stage   submitted
Date   2019-08-28
Version   v4
Language   en ?
arXiv  1809.09280v4
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