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COFINAL TYPES BELOW
$\aleph _\omega $
- Part of
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- Journal:
- The Journal of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 24 July 2023, pp. 1-26
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- Article
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It is proved that for every positive integer n, the number of non-Tukey-equivalent directed sets of cardinality
$\leq \aleph _n$ is at least 
$c_{n+2}$, the 
$(n+2)$-Catalan number. Moreover, the class 
$\mathcal D_{\aleph _n}$ of directed sets of cardinality 
$\leq \aleph _n$ contains an isomorphic copy of the poset of Dyck 
$(n+2)$-paths. Furthermore, we give a complete description whether two successive elements in the copy contain another directed set in between or not.
Introduction
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- Book:
- Slenderness
- Published online:
- 30 November 2018
- Print publication:
- 06 December 2018, pp 1-40
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