Speaker: Santi Spadaro, University of Sao Paulo.
Time and Date: Monday, November 3 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.
In this second lecture we will show how to use Chang's Conjecture for aleph_omega to destroy cofinal sparse families in ([\aleph_\omega]^\omega, \subseteq) and discuss how much sparseness we can get in ZFC for cofinal subfamilies of this partial order."
Time and Date: Monday, November 3 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.
In this second lecture we will show how to use Chang's Conjecture for aleph_omega to destroy cofinal sparse families in ([\aleph_\omega]^\omega, \subseteq) and discuss how much sparseness we can get in ZFC for cofinal subfamilies of this partial order."