Thank you, that was very interesting. I was surprised at the definition of the basic open sets because they felt quite closed to my intuition, so the topology feels discrete to me. It’s definitely Hausdorff, I guess, but that’s no big deal. I’m guessing if you’re saying it uses a lot of the axioms, it uses the axiom of choice. It feels like that kind of arena, but I’m no set theorist. Having been taught by ring theorists, I always found the axiom of choice no big deal and totally uncontroversial, but I’m aware of the existence of mathematicians who feel otherwise, intuitionists (confusing name) and constructivists and the like. Do set theorists have a lot of debate about axioms, is it largely led by consensus, or deeply controversial, or just a case of making clear which you’re using and no one gets excited about it?
Thank you, that was very interesting. I was surprised at the definition of the basic open sets because they felt quite closed to my intuition, so the topology feels discrete to me. It’s definitely Hausdorff, I guess, but that’s no big deal. I’m guessing if you’re saying it uses a lot of the axioms, it uses the axiom of choice. It feels like that kind of arena, but I’m no set theorist. Having been taught by ring theorists, I always found the axiom of choice no big deal and totally uncontroversial, but I’m aware of the existence of mathematicians who feel otherwise, intuitionists (confusing name) and constructivists and the like. Do set theorists have a lot of debate about axioms, is it largely led by consensus, or deeply controversial, or just a case of making clear which you’re using and no one gets excited about it?