czgnome

4 ms·

1. 1.▲
   by czgnome 7mo ago

   I studied commutative algebra. I’m not set theorist. I wasn’t sure exactly what “set theoretically indiscernible” meant.
2. 2.▲
   by czgnome 7mo ago

   If two things are set theoretically indistinguishable then one can’t say “pick one and call it i and the other one -i”. The two sets are the same according to the background set theory.
3. 3.▲
   by czgnome 7mo ago

   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 ordina
4. 4.▲
   by czgnome 7mo ago

   Your view of the complex numbers is the rigid one. Now suppose you are given a set with two binary operations defined in such a way that the operations behave well with each other. That is you have a ring. Suppose that by some process you
5. 5.▲
   by czgnome 7mo ago

   This would be the rigid interpretation since i and -i are concrete distinguishable elements with Im and Re defined.
6. 6.▲
   by czgnome 7mo ago

   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.