Morasses, semimorasses and supercompact ultrafilters
type: Item
instance of: scholarly article
title: Morasses, semimorasses and supercompact ultrafilters
zbMATH Open document ID: 1399.03011
author: Juan-Miguel Gracia
published in: Acta Mathematica Hungarica
publication date: 2018-02-13T00:00:00Z
review text: The author shows that a \((\kappa,\lambda)\)-semimorass on \(\mathcal P_\kappa\lambda\) and a \((\kappa,1)\)-simplified morass on \(\mathcal P_\kappa\kappa^+\), where \(\kappa\) is suitable supercompact can be a member of a supercompact ultrafilter on \(\mathcal P_\kappa\lambda\) or \(\mathcal P_\kappa\kappa^+\) respectively. As an application, there is a model of the negation of the singular cardinals hypothesis in which products of the form \(\prod_n\kappa_n^{+\alpha+1}\) have scales with lots of structure.
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E04
Mathematics Subject Classification ID: 03E10
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 6837926
zbMATH Keywords: morass
zbMATH Keywords: semimorass
zbMATH Keywords: supercompact cardinal
zbMATH Keywords: tree-like scale
MaRDI profile type: Publication
full work available at URL: s10474-017-0708-4
OpenAlex ID: W2598409831
cites work: Tight stationarity and tree-like scales
cites work: Continuous tree-like scales
cites work: Q3724320
cites work: On a question of Pereira
cites work: The fine structure of the constructible hierarchy
cites work: Q3535899
cites work: Semimorasses and nonreflection at singular cardinals
cites work: Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
cites work: Consistency Results Concerning Supercompactness
cites work: The PCF conjecture and large cardinals
cites work: S-forcing. I: a ''black-box'' theorem for morasses, with applications to super-Souslin trees
cites work: Morasses, diamond, and forcing
cites work: Simplified morasses
cites work: Q3221976
DOI: 10.1007/S10474-017-0708-4
description: scientific article; zbMATH DE number 6837926