# Dilip Raghavan: An application of PCF theory to cardinal invariants above the continuum

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 24 January 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Dilip Raghavan

Title: An application of PCF theory to cardinal invariants above the continuum

Abstract: It will be proved in ZFC that if kappa
is any regular cardinal greater than beth_omega, then
d(kappa) leq r(kappa). Here d(kappa) is the
smallest size of dominating family of functions from kappa
to kappa and r(kappa) is the smallest size of a family
of subsets of kappa which decide every other subset of kappa.
This result partially dualizes an earlier result
of myself and Shelah. The proof uses the revised GCH,
which is an application of PCF theory.
This is joint work with Shelah.