Partial near supercompactness
type: Item
instance of: scholarly article
title: Partial near supercompactness
zbMATH Open document ID: 1261.03148
author: Jason Aaron Schanker
published in: Annals of Pure and Applied Logic
publication date: 2012-11-29T00:00:00Z
review text: The author introduces a refinement of the levels of supercompactness, called near supercompactness. A cardinal \(\kappa\) is \textit{nearly \(\lambda\)-supercompact} if for every \(A \subset \lambda\) there is a transitive model \(M\) of ZFC minus the power set axiom (with collection used instead of replacement), closed under sequences of length less than \(\kappa\) and containing \(A\), \(\kappa\), and \(\lambda\), and a transitive \(N\), and an elementary embedding \(j: M \to N\) with critical point \(\kappa\) such that \(j(\kappa) > \lambda\) and \(j''\lambda \in N\). It interleaves as follows: any cardinal that is \(\lambda\)-supercompact is also nearly \(\lambda\)-supercompact, and conversely a cardinal that is nearly \(2^{\lambda^{<\kappa}}\)-supercompact is \(\lambda\)-supercompact. The author then generalizes indestructibility results as well as the construction of a Laver diamond to this new hierarchy.
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 6111171
zbMATH Keywords: near supercompactness
zbMATH Keywords: indestructibility
zbMATH Keywords: determinacy
zbMATH Keywords: failure of GCH
zbMATH Keywords: Laver diamond
MaRDI profile type: Publication
full work available at URL: j.apal.2012.08.001
OpenAlex ID: W2085381255
DOI: 10.1016/J.APAL.2012.08.001
description: scientific article; zbMATH DE number 6111171