I know that it's established that non-measurable sets cannot be constructed without the axiom of choice but I was wondering if countable choice was enough? Since the ones that I have seen use uncountable choice.
My intuition tells me no. Since I tend to think of measurable sets as being closed under "countable operations". Although if we're being precise the operations in question are unions, intersections and complements; so i was wondering if we can use countable choice in some way to construct a non-measurable set.