Well ordered subsets of linearly ordered sets
type: Item
instance of: scholarly article
title: Well ordered subsets of linearly ordered sets
zbMATH Open document ID: 0827.03029
published in: Notre Dame Journal of Formal Logic
publication date: 1995-07-03T00:00:00Z
review text: The authors investigate the strength of Davis' theorem LFC in the hierarchy of weak choice principles. LFC is the assertion that linear orders with the fixed point property for monotone mappings are complete. LFC is in strength between CF and DS. Here CF is the axiom that every linearly ordered set has a cofinal well-ordered subset. DS is the statement that a linear ordering without an infinite descending subsequence is a well-ordering. The main result of the paper is the construction of Fraenkel-Mostowski permutation models which show that DS does not imply LFC and LFC does not imply CF.
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 06A05
zbMATH DE Number: 769233
zbMATH Keywords: hierarchy of weak choice principles
zbMATH Keywords: LFC
zbMATH Keywords: linear orders
zbMATH Keywords: fixed point property
zbMATH Keywords: CF
zbMATH Keywords: DS
zbMATH Keywords: well-ordering
zbMATH Keywords: Fraenkel-Mostowski permutation models
author: Hartmut F. W. Hoeft
author: Paul Howard
reviewed by: Norbert Brunner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040511347
OpenAlex ID: W1972055552
cites work: A characterization of complete lattices
cites work: A Class of ‘Near‐Finite’ Order‐Types
cites work: Definitions of finite
cites work: The axiom of choice
cites work: Set theory. An introduction to independence proofs
cites work: Q4205442
cites work: Q3960633
cites work: Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods
DOI: 10.1305/NDJFL/1040511347
description: scientific article; zbMATH DE number 769233