Hacker News Reader

Note though, that nonstandard analysis isn't compatible with more "intuitionistic" https://en.wikipedia.org/wiki/Axiom_of_determinacy (in place of axiom on choice), which free you from Banach–Tarski paradox and have some other appealing properties.

View on HN

On the contrary, in an intuitionistic setting you can use https://en.wikipedia.org/wiki/Synthetic_differential_geometr... and https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis which aren't nearly as easy to phrase classically. (Sure you can phrase things in terms of toposes, but that's just a roundabout way of saying that you're operating in a constructive setting.)

Can do it in pure ZF:

https://www.youtube.com/watch?v=YE68yptMMeQ

https://u.cs.biu.ac.il/~katzmik/spot.html

Reply on news.ycombinator.com