Extender-based Magidor-Radin forcing
type: Item
instance of: scholarly article
title: Extender-based Magidor-Radin forcing
zbMATH Open document ID: 1218.03032
author: Carmi Merimovich
published in: Israel Journal of Mathematics
publication date: 2011-05-05T00:00:00Z
review text: From the author's introduction: ``The general theme of the forcing notion we present is as follows. Given a Mitchell increasing extender sequence, \(2^{\kappa}\) is controlled by the size of the extenders, the cofinality of \(\kappa\) is controlled by the length of the sequence, and a club is added to \(\kappa\) so that the power and cofinality of cardinals in the club is controlled by reflections of the extender sequence. In the generic extension \(\kappa\) can become singular, can remain regular, or measurable.'' The paper begins with the definition of extender-based Prikry forcing, which will play a role in the ultimate definition of extender-based Magidor-Radin forcing. The ideas used in the definition of Magidor-Radin forcing are then illustrated via extender-based Magidor forcing using two extenders. The reader is expected to be acquainted with large cardinals, especially with extenders, measures, and elementary embeddings, and of course with forcing.
reviewed by: J. M. Plotkin
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 5884631
zbMATH Keywords: forcing
zbMATH Keywords: extenders
zbMATH Keywords: Mitchell increasing extender sequence
zbMATH Keywords: extender-based Prikry forcing
zbMATH Keywords: extender-based Magidor-Radin forcing
MaRDI profile type: Publication
full work available at URL: s11856-011-0038-0
OpenAlex ID: W2008381487
cites work: Coherent sequences versus Radin sequences
cites work: Q4694295
cites work: Power function on stationary classes
cites work: Supercompact extender based Prikry forcing
cites work: Extender-based Radin forcing
cites work: Q3960838
cites work: Q5613932
cites work: Adding closed cofinal sequences to large cardinals
DOI: 10.1007/S11856-011-0038-0
description: scientific article; zbMATH DE number 5884631