Cichoń's maximum without large cardinals
type: Item
instance of: scholarly article
title: Cichoń's maximum without large cardinals
DOI: 10.4171/JEMS/1178
author: Jakob Kellner
author: S. Shelah
author: Martin Goldstern
author: Diego Alejandro Mejía
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2022-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1906.06608
review text: Summary: Cichoń's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and \(\sigma\)-compact subsets of the irrationals. It is consistent that all entries of Cichoń's diagram are pairwise different (apart from \(\mathrm{add}(\mathcal{M})\) and \(\mathrm{cof}(\mathcal{M})\), which are provably equal to other entries). However, the consistency proofs so far required large cardinal assumptions. In this work, we show the consistency without such assumptions.
Mathematics Subject Classification ID: 03E17
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 7608245
zbMATH Keywords: set theory
zbMATH Keywords: forcing
zbMATH Keywords: Cichoń's diagram
MaRDI profile type: Publication
cites work: Additivity of Measure Implies Additivity of Category
cites work: Q4844091
cites work: The Cichoń diagram
cites work: Larger Cardinals in Cichon's Diagram
cites work: Filter-linkedness and its effect on preservation of cardinal characteristics
cites work: On cardinal characteristics of Yorioka ideals
cites work: On Dense Subsets of the Measure Algebra
cites work: THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
cites work: Creature forcing and five cardinal characteristics in Cichoń's diagram
cites work: COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS
cites work: Consistency of the Continuum Hypothesis. (AM-3)
cites work: Cichoń's maximum
cites work: Controlling cardinal characteristics without adding reals
cites work: Preservation of splitting families and cardinal characteristics of the continuum
cites work: The left side of Cichoń's diagram
cites work: The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing)
cites work: Iterations of Boolean algebras with measure
cites work: Another ordering of the ten cardinal characteristics in Cichoń's diagram
cites work: COMPACT CARDINALS AND EIGHT VALUES IN CICHOŃ’S DIAGRAM
cites work: Set theory.
cites work: Matrix iterations and Cichon's diagram
cites work: Some Properties of Measure and Category
cites work: Additivity of Measure Implies Dominating Reals
cites work: Many different covering numbers of Yorioka's ideals
cites work: Q3342556
cites work: The strength of measurability hypotheses
description: scientific article; zbMATH DE number 7608245