[_0w8t]

EDIT to clarify the parent comment. Essentially the paper claims that using classical mathematical analysis (which is the constructive analysis plus the Axiom of Choice) when interpreting the equations of physical models is poor choice. It is better to use intuition mathematical analysis (which is the constructive analysis plus axioms of choice sequence) as it provides better match with our intuition.

But for me the extra axioms are still arbitrary. As all our measurements have finite precision, all those extra axioms does not matter in real calculations. If some extra axioms helps to discover results that are also applicable to the world of finite precision, then go for it. But not claim that the world is such.