Hausdorff gaps and towers in $\mathcal {P}(\omega )/ {\rm Fin}$

Piotr Borodulin-Nadzieja; David Chodounský

doi:10.4064/fm229-3-1

Geodesic

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Hausdorff gaps and towers in $\mathcal {P}(\omega )/ {\rm Fin}$

Piotr Borodulin-Nadzieja ¹ ; David Chodounský ²

¹ Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
² Institute of Mathematics AS CR Žitná 25 115 67 Praha 1, Czech Republic and Department of Mathematics York University 4700 Keele Street Toronto, Ontario M3J 1P3, Canada

Fundamenta Mathematicae, Tome 229 (2015) no. 3, pp. 197-229.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

We define and study two classes of uncountable $\subseteq ^*$-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.

DOI : 10.4064/fm229-3-1

Keywords: define study classes uncountable subseteq * chains hausdorff towers suslin towers discuss their existence various models set theory results methods provide examples indestructible gaps equivalent hausdorff gap indicate possible ways developing structure theory towers based classification their tukey types

Affiliations des auteurs :

Piotr Borodulin-Nadzieja ¹ ; David Chodounský ²

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Piotr Borodulin-Nadzieja; David Chodounský. Hausdorff gaps and towers in $\mathcal {P}(\omega )/ {\rm Fin}$. Fundamenta Mathematicae, Tome 229 (2015) no. 3, pp. 197-229. doi : 10.4064/fm229-3-1. http://geodesic.mathdoc.fr/articles/10.4064/fm229-3-1/

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