Speaker: Santi Spadaro, University of Sao Paulo.
Time and Date: Monday October 20 at 2PM. Room: 266A.
Abstract: "Sparse families are a set-theoretic tool that provides the combinatorial skeleton for many seemingly unrelated problems from various areas of mathematics. For example, Kojman, Milovich and I used them to find bounds for the cardinality of bounded subsets in certain topological bases and Blass used them to find bounds for the cardinality of the divisible part of certain quotient groups. A family of countable sets of a given cardinal is sparse if every uncountable subfamily has uncountable union. Good PCF scales yield large sparse families, while variants of Chang Conjecture can be used to destroy them. In this first lecture we will focus on how to construct large sparse families."
Time and Date: Monday October 20 at 2PM. Room: 266A.
Abstract: "Sparse families are a set-theoretic tool that provides the combinatorial skeleton for many seemingly unrelated problems from various areas of mathematics. For example, Kojman, Milovich and I used them to find bounds for the cardinality of bounded subsets in certain topological bases and Blass used them to find bounds for the cardinality of the divisible part of certain quotient groups. A family of countable sets of a given cardinal is sparse if every uncountable subfamily has uncountable union. Good PCF scales yield large sparse families, while variants of Chang Conjecture can be used to destroy them. In this first lecture we will focus on how to construct large sparse families."