Large free linear algebras of real and complex functions

Artur Bartoszewicz, Szymon Gł\cab, Adam Paszkiewicz

Let $X$ be a set of cardinality $\kappa$ such that ${\kappa }^{\omega }=\kappa$. We prove that the linear algebra ${\mathbb{R}}^X$ (or ${\mathbb{C}}^X$) contains a free linear algebra with $2^{\kappa }$ generators. Usi…