# David Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem, IV

Thursday, November 3, 2016, from 4 to 5:30pm
East Hall, room 3096

Speaker: David Fernández Bretón (University of Michigan)

Title: Strong failures of higher analogs of Hindman’s theorem, IV

Abstract:

This is talk 4 out of 4. Last time we introduced a set-theoretic principle S(kappa,theta), which implies a particular anti-Ramsey theoretic result on all groups of cardinality kappa. In this talk we will prove that S(omega_1,omega_1) holds, and also that S(kappa,omega) holds whenever kappa has uncountable cofinality equals the cofinality of the powerset of a cardinal lambda such that lambda^{<lambda}=lambda (this last result has a nice implication for the additive group of real numbers).