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Around the definability of mad families

Presented by: 
A D Törnquist [Københavns Universitet]
Date: 
Monday 24th August 2015 - 15:00 to 16:00
Venue: 
INI Seminar Room 1
Abstract: 
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 $\omega$.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons