The short extenders gap three forcing using a morass
type: Item
instance of: scholarly article
title: The short extenders gap three forcing using a morass
zbMATH Open document ID: 1217.03035
author: Carmi Merimovich
published in: Archive for Mathematical Logic
publication date: 2011-03-02T00:00:00Z
review text: \textit{M. Gitik} [``Blowing up the power of a singular cardinal -- wider gaps'', Ann. Pure Appl. Logic 116, No. 1--3, 1--38 (2002; Zbl 0997.03042)] proved the following: Assume the GCH. Let \(\langle \kappa_n : n<\omega\rangle\) be an increasing sequence of cardinals such that, for each \(n\), there is a \(\langle \kappa_n, \kappa_n^{+n+3}\rangle\)-extender, and let \(\kappa = \bigcup_{n<\omega} \kappa_n\). Then there is a cardinal-preserving generic extension adding no new bounded subsets to \(\kappa\) in which \(2^\kappa = \kappa^{+3}\). The author reproves this result using a neat stationary \(\langle \kappa^{++}, 1\rangle\)-simplified morass to define the forcing notion and show it is of Prikry type.
reviewed by: Pierre Matet
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 5859285
zbMATH Keywords: singular cardinal hypothesis
zbMATH Keywords: Prikry property
zbMATH Keywords: extender-based forcing
zbMATH Keywords: simplified morass
MaRDI profile type: Publication
full work available at URL: s00153-010-0204-9
OpenAlex ID: W2065841005
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DOI: 10.1007/S00153-010-0204-9
description: scientific article; zbMATH DE number 5859285