Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Jing Zhang

CMU

Title: Poset dimension and singular cardinals

Abstract:

The dimension of a poset (P, ≤P) is defined as the least cardinal λ such that there exists a λ-sized collection of linear extensions of P realizing P, that is to say a ≤P b if and only a ≤ b in any linear extension in the collection. We will focus on the poset Pα(κ), that is the poset of subsets of κ of size less than α partially ordered by inclusion, and determine completely the dimension of such posets under GCH. Then we will mention a few consistency results when GCH fails. In particular, we point out the connection between the dimension of the poset Pα (2κ) and the density of 2κ under the <α-box product topology, and show it is consistent that they are different.