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Around the definability of mad families

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Mathematical, Foundational and Computational Aspects of the Higher Infinite

I will talk about my new proof that there are no analytic infinite mad (maximal almost disjoint) families of subsets of $omega$, a result originally proved by A.D.R. Mathias in his famous “Happy Families” paper. The new proof motivates a proof that there are no infinite mad families in Solovay’s model. If time permits, I will also talk about the differences between mad families of subsets of $omega$ and other types of mad families, such as eventually different families of functions from $omega$ to $omega$, and why these problems may be very different from the situation presented by mad families of subsets of $omega$.

This talk is part of the Isaac Newton Institute Seminar Series series.

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