Hausdorff gaps and towers in 𝓟(ω)/Fin

Piotr Borodulin-Nadzieja, and David Chodounský. "Hausdorff gaps and towers in 𝓟(ω)/Fin." Fundamenta Mathematicae 229.3 (2015): 197-229. <http://eudml.org/doc/283319>.

@article{PiotrBorodulin2015,
abstract = {We define and study two classes of uncountable ⊆*-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.},
author = {Piotr Borodulin-Nadzieja, David Chodounský},
journal = {Fundamenta Mathematicae},
keywords = {hausdorff gaps; special gaps; towers; oscillations; Suslin trees; tukey order},
language = {eng},
number = {3},
pages = {197-229},
title = {Hausdorff gaps and towers in 𝓟(ω)/Fin},
url = {http://eudml.org/doc/283319},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Piotr Borodulin-Nadzieja
AU - David Chodounský
TI - Hausdorff gaps and towers in 𝓟(ω)/Fin
JO - Fundamenta Mathematicae
PY - 2015
VL - 229
IS - 3
SP - 197
EP - 229
AB - We define and study two classes of uncountable ⊆*-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.
LA - eng
KW - hausdorff gaps; special gaps; towers; oscillations; Suslin trees; tukey order
UR - http://eudml.org/doc/283319
ER -