>>11257051Choice is an intuitive and useful property of finite and (less clear) countable sets that historically has been introduced to set theory and was freely used by algebraist and analysts in the guise of short-cut existence claims like well ordering functions and other bottom element existence claims - they wouldn't give it away anymore. In reality, its consequences are highly non-computable in uncountable cardinalities (reals and bigger), so in effect its use kept on giving math a bloomy flavor - even after Turing's works on non-computability and the rise of CS. Our foundations kept the disciplines apart.
The non-effectiveness of such axioms gets worse the higher up you go in Cantors constructions.
So If you postulate existence of large cardinals, you expand what ought to be realized in the set theoretical universe, while at the same time, with AoC, you formally break it down and postulate the stuff "up there" is still rather close, conceptually, at the finite sets you started with.
