[czgnome]

In the article he says there is a model of ZFC in which the complex numbers have indistinguishable square roots of -1. Thus that model presumably does not allow for a rigid coordinate view of complex numbers.

[yorwba]

It just means that there are two indistinguishable coordinate views a + bi and a - bi, and you can pick whichever you prefer.

[czgnome]

Theorem. If ZFC is consistent, then there is a model of ZFC that has a definable complete ordered field ℝ with a definable algebraic closure ℂ, such that the two square roots of −1 in ℂ are set-theoretically indiscernible, even with ordinal parameters.

Haven’t thought it through so I’m quite possibly wrong but it seems to me this implies that in such a situation you can’t have a coordinate view. How can you have two indistinguishable views of something while being able to pick one view?