*I would guess that the paradox disappears if one can replace the axiom of choice …*

Hi Matti. At the end of the book, Wagon discusses the close relation between AC and the paradox: one can show that the paradox is unprovable in ZF alone, so it really hinges on AC. In the topos **Set**, AC is a simple condition but not one of the elementary axioms, so it is easy enough in higher topos theory to work without AC. I like this idea for many reasons.

I would guess that the paradox disapperas if one can replace the axiom of choice with a weaker form restricting the choice to rationals or algebraics. This kind

of restriction of course makes sense only in a very special case when one has symmetries so that one can specify the preferred coordinates with respect to which the notion of rational point is defined.