Answering a question raised by Luis Pereira, we show that a continuous tree-like scale can exist above a supercompact cardinal. We also show that the existence of a continuous tree-like scale at ℵω is consistent with Martin’s Maximum.
@article{bwmeta1.element.doi-10_2478_s11533-010-0001-z,
author = {James Cummings},
title = {Continuous tree-like scales},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {314-318},
zbl = {1207.03052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0001-z}
}
James Cummings. Continuous tree-like scales. Open Mathematics, Tome 8 (2010) pp. 314-318. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0001-z/
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