Ralf Schindler: A Hamel basis for the reals without choice

09 January: 16.30
seminar room 0.008
Mathematisches Institut
Universität Bonn
Endenicher Allee 60

Ralf Schindler (Münster) – A Hamel basis for the reals without choice

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 in N. This is joint work with Liuzhen Wu and Liang Yu, inspired by earlier joint work with Mariam Beriashvili. DC fails in N, and it remains open if in the base theory ZF+DC, the existence of a Hamel basis implies that the reals can be wellordered.

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