On strong chains of uncountable functions
type: Item
instance of: scholarly article
title: On strong chains of uncountable functions
zbMATH Open document ID: 0961.03039
DOI: 10.1007/BF02803525
author: Piotr Koszmider
published in: Israel Journal of Mathematics
publication date: 2001-01-25T00:00:00Z
review text: Let \(f,g:\omega_1\rightarrow \omega_1\). Define \(f\ll g\) if and only if \(\{\xi\in\omega_1 : f(\xi)\geq g(\xi)~\}\) is finite. Answering a question of A. Hajnal, the author proves that the following is consistent: there is a well-ordered, increasing \(\ll\)-chain of length \(\omega_2\). The author uses his method of forcing with side conditions in morasses to establish this consistency result. Assuming CH, he also proves that no c.c.c forcing would give such a chain. The paper is meant to be self-contained.
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 1506591
zbMATH Keywords: morasses
zbMATH Keywords: forcing with side conditions
zbMATH Keywords: c.c.c. forcing
zbMATH Keywords: well-ordered chains
zbMATH Keywords: consistency
reviewed by: J. M. Plotkin
MaRDI profile type: Publication
cites work: Almost-disjoint sets the dense set problem and the partition calculus
cites work: Q3337413
cites work: Remarks on superatomic Boolean algebras
cites work: Aspects of constructibility
cites work: Some principles related to Chang's conjecture
cites work: The fine structure of the constructible hierarchy
cites work: Set theory. An introduction to independence proofs
cites work: Q3039339
cites work: Semimorasses and nonreflection at singular cardinals
cites work: On the existence of strong chains in ℘(ω1)/Fin
cites work: Adding dominating functions mod finite
cites work: Subsets of \({}^ \omega\omega\) and the Fréchet-Urysohn and \(\alpha_ i\)-properties
cites work: Height and Width of Superatomic Boolean Algebras
cites work: Q4848578
cites work: Directed Sets and Cofinal Types
cites work: Partitioning pairs of countable ordinals
cites work: Partition Problems in Topology
cites work: Remarks on Martin's Axiom and the Continuum Hypothesis
cites work: Morasses, diamond, and forcing
cites work: Simplified morasses
cites work: Strongly almost disjoint functions
cites work: 𝑃_{𝑘}𝜆 combinatorics. I. Stationary coding sets rationalize the club filter
description: scientific article; zbMATH DE number 1506591