Subtle cardinals and linear orderings
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.
scientific article; zbMATH DE number 1562989