Subtle cardinals and linear orderings
type: Item
instance of: scholarly article
title: Subtle cardinals and linear orderings
zbMATH Open document ID: 0966.03048
DOI: 10.1016/S0168-0072(00)00019-1
author: Harvey M. Friedman
published in: Annals of Pure and Applied Logic
publication date: 2001-07-24T00:00:00Z
review text: The author begins with a self-contained introduction to the large cardinals called \(k\)-subtle, \(k\)-almost ineffable, and \(k\)-ineffable (\(1\leq k <\omega\)). These families were introduced by Baumgartner in 1975. Following Baumgartner, in section 1 the author shows that these families ``define three properly intertwined hierarchies with the same limit, lying strictly above total indescribability and strictly below arrowing \(\omega\).'' In section 2, the author goes on to characterize the subtle hierarchy by means of elementary properties that mention neither closed unbounded sets nor stationary sets. The main result of the paper is a characterization of this hierarchy by a second order property (\(k\)-critical) of linear orderings.
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 1562989
zbMATH Keywords: set theory
zbMATH Keywords: large cardinal hierarchy
zbMATH Keywords: Ramsey theory
Wikidata QID: Q55895926
reviewed by: J. M. Plotkin
MaRDI profile type: Publication
cites work: Q4071748
cites work: Q4149456
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DBLP publication ID: journals/apal/Freidman01
description: scientific article; zbMATH DE number 1562989