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HAPPY AND MAD FAMILIES IN L(ℝ)
Published online by Cambridge University Press: 01 August 2018
Abstract
We prove that, in the choiceless Solovay model, every set of reals is H-Ramsey for every happy family H that also belongs to the Solovay model. This gives a new proof of Törnquist’s recent theorem that there are no infinite mad families in the Solovay model. We also investigate happy families and mad families under determinacy, applying a generic absoluteness result to prove that there are no infinite mad families under $A{D^ + }$.
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- Copyright © The Association for Symbolic Logic 2018
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