A $\kappa $-rough morass under $2^{{<}\kappa }=\kappa $ and various applications
Volume 248 / 2020
Fundamenta Mathematicae 248 (2020), 111-133
MSC: Primary 03C30, 03E30, 03E35, 03E45, 03E55, 03E75; Secondary 03C55, 03D60, 03E65.
DOI: 10.4064/fm387-4-2019
Published online: 18 October 2019
Abstract
Let $\kappa $ be an uncountable regular cardinal. Assuming $2^{ \lt \kappa}=\kappa $, we construct a $\kappa $-rough morass. As an immediate consequence, we prove the Gap-1 cardinal transfer theorem under $2^{ \lt \kappa}=\kappa $. We examine how this affects the consistency strength of this transfer problem. We also present several applications of our rough morass.
