Chang's conjecture for \(\aleph_\omega\)
type: Item
instance of: scholarly article
title: Chang's conjecture for \(\aleph_\omega\)
zbMATH Open document ID: 0696.03023
DOI: 10.1007/BF02937302
author: Jean-Pierre Levinski
author: Menachem Magidor
author: S. Shelah
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: From huge-like large cardinal assumptions, the relative consistency of \((\aleph_{\omega_ n+1},\aleph_{\omega_ n})\twoheadrightarrow (\aleph_{k+1},\aleph_ k)\) for \(k=n<\omega\) or \(k+1<n<\omega\) is shown (with GCH). Under GCH, a simple argument shows that the case \(n<k\) is false. Open remains the case when \(k+1=n\).
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03C55
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 4139730
zbMATH Keywords: gap-one two-cardinal models
zbMATH Keywords: Chang's conjecture
zbMATH Keywords: transfer properties
zbMATH Keywords: GCH
Wikidata QID: Q123141231
reviewed by: Péter Komjáth
MaRDI profile type: Publication
cites work: Q3944594
cites work: On the consistency strength of ''accessible'' Jonsson cardinals and of the weak Chang conjecture
cites work: Some Stationary Subsets of (λ)
cites work: Some principles related to Chang's conjecture
cites work: Large Cardinals and Strong Model Theoretic Transfer Properties
cites work: Saturated ideals
cites work: Instances of the conjecture of Chang
cites work: Some strong axioms of infinity incompatible with the axiom of constructibility
cites work: Proper forcing
description: scientific article; zbMATH DE number 4139730