Ralf Schindler: A Hamel basis for the reals without choice

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.

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