I will give a brief overview of theory of the possible spectra of various combinatorial families such as mad families, independent families and other similar families. In particular I will detail the proof that there are no mad families of intermediate size in the Cohen model as an introduction to isomorphism-of-names arguments. Finally, I will sketch recent work of how to realise uncountable spectra of \(a_T\), i.e. given an uncountable set \(C\) of cardinals (with some necessary extra assumptions) how to construct a model which has partitions of Baire space into compact sets of exactly the sizes prescribed in \(C\).
Spectra of combinatorial families
29.06.2023 11:30 - 12:59
Organiser:
KGRC
Location: