There are seven days until Christmas. Every day, I will cancel one axiom of set theory, until there are no more axioms, and set theory will be cancelled altogether
A new day, another axiom cancelled. Today's cancellation is the axiom of infinity. There are so many ways of making infinite sets, why did they choose x ∪ {x} as the successor? Why not ℘(x)? They're cowards, that's why. So what if ℘⁶(∅) can't be physically written down, that is no concern of the mathematician.
🚫 infinity 🚫
We're more than halfway there. Today we're cancelling the axiom of foundation. That's right, Zermelo and Frankel's precious well-foundedness? Yeet that in the trash. There is no reason a set should not contain itself; coinductive structures are just as valid as inductive ones. It's co-discrimination!
🚫 foundation 🚫
I'm very but I have a duty and that is to cancel another set theory axiom. This time I'm cancelling the axiom schema of replacement for being too complicated and confusing. It's hard to figure out what to instantiate the formula inside of it as, and it's not intuitive in its pure set statement, and it's only clear that it's the image of a function when you use classes. It's also a very big axiom and I think they can stand to break it up into small pieces.
🚫 replacement 🚫
We've come down to the last few axioms now. I'm so sorry, but I have to cancel the axiom of powerset. You can't make some infinite cardinalities bigger than others if there aren't any more of them, I guess (and we already cancelled infinity, so there aren't infinite ones at all). But happy Christmas Adam!
🚫 powerset 🚫
@ionchy i would simply construct a well-ordering on ℝ and pick the least element
@ionchy 🚫∅🚫
@ionchy finally we are free
@ionchy next step is to cancel the rest of math
@ionchy I am so here for this
@ionchy cant wait
@ionchy This sounds like a threat. "Unless my demands are met set theory will be no more in 7 days."
@jordyd oh, I have no demands. my only demand is that set theory be cancelled by Christmas, even if I have to do it myself
Today, we are cancelling the axiom of pairing. Who needs pairing? You have replacement. There's no reason making a set of two sets should be handled any more specially than making a set of many sets.
🚫 pairing 🚫