i decided to put my blog's source on Gist. still under maintenance. gist.github.com/yuuki15/6f4dd4…
posted at 23:13:30
I've uploaded some of my videos etc to archive.org. hope they will remain until a future where youtube is gone. archive.org/search?query=c…
posted at 16:27:36
¹ this indicates "direct implications or relative consistency implications", tho. (e.g., huge < supercompact) in order of both size and strength: • inaccessible < measurable < huge < rank-into-rank < 0=1
posted at 06:20:22
in the large picture, • the size of a number is proportional to • how many numbers it can prove to be consistent. the largest number proves the consistency of all numbers, including itself. by Gödel's theorem, it is a "contradiction".
posted at 04:04:38
let us write Fin + Inf as ZFC. similarly, if we add "a large cardinal exists", then we can prove the consistency of ZFC. • ZFC + LC ⊢ Con(ZFC)
posted at 04:02:04
by Gödel's second incompleteness theorem, the axioms "finite numbers exist" can't prove their own consistency. • Fin ⊬ Con(Fin) now if we add "ℵ₀ exists", then we can prove the consistency of finite numbers. • Fin + Inf ⊢ Con(Fin) this shows Fin + Inf > Fin.
posted at 03:59:23
