Abstract
AbstractWe prove that, in the choiceless Solovay model, every set of reals isH-Ramsey for every happy familyHthat 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$A{D^ + }$.
Publisher
Cambridge University Press (CUP)
Reference29 articles.
1. DERIVED MODELS ASSOCIATED TO MICE
2. Universally Baire Sets of Reals
3. [5] Chan W. and Magidor M. , When an equivalence relation with all borel classes will be borel somewhere?, preprint, 2016, arXiv:1608.04913.
4. A trichotomy theorem in natural models of 𝐴𝐷⁺
5. Filters and games
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