BARCELONA SET THEORY SEMINAR

Date: Monday 30 October 2017

Time: 16:00

Place: IMUB*

University of Barcelona

Gran Via de les Corts Catalanes 585

08007 Barcelona

Speaker: Ralf Schindler

Title: A Hamel basis for the reals without choice (Universität Münster)

Abstract: The Cohen-Halpern-Levy model N has an infinite set of

reals without a countable subset. Answering a question of D.

Pincus and K. Prikry from 1975, we show that there is a Hamel

basis (i.e., a basis for R as a vector space over Q) in N. This is

joint work with Liuzhen Wu and Liang Yu, inspired by earlier joint

work with Mariam Beriashvili. The axiom of Dependent Choice

(DC) fails in N, but in later joint work with Wu and Yu we also

showed that there is a model of ZF+DC with a Hamel basis and in

which the reals cannot be wellordered.