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A $\kappa $-rough morass under $2^{{<}\kappa }=\kappa $ and various applications

Volume 248 / 2020

Luis Miguel Villegas Silva 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


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.


  • Luis Miguel Villegas SilvaDepartamento de Matemáticas
    Universidad Autónoma Metropolitana Iztapalapa
    Av. San Rafael Atlixco 186, Col. Vicentina
    09340 Iztapalapa, CDMX, Mexico

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