Special Session
Independence for uncountable cardinals
On-site
In this talk, we will discuss the concept of maximal independent families for uncountable cardinals. First, we will mention a summary of results regarding the existence of such families in the case of an uncountable regular cardinal. Specifically, we will focus on joint work with Vera Fischer regarding the existence of an indestructible maximal independent family, which turns out to be indestructible after forcing with generalized Sacks forcing.
In the second part, we will focus on the singular case and present two results obtained in joint work with Omer Ben-Neria. Finally, I will mention some open questions and future paths of research.
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