The <restricted axiom of choice> $\mathsf{AC}_X(Y)$ says that for every $X$-indexed family $(A_x)_{x\in X}$ of nonempty <subset>[subsets] of $Y$, there is a <choice function> $c:X\to Y$ such that $c(x)\in A_x$ for every $x\in X$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 158 / 1 / ii / Solution

{title2=$\mathsf{AC}_X(Y)$}

For sets $X$ and $Y$, $\mathsf{AC}_X(Y)$ says that every $X$-indexed family $(A_x)_{x\in X}$ of nonempty subsets of $Y$ has a <choice function> $c:X\to Y$ satisfying $c(x)\in A_x$.

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 Incoming links: Restricted axiom of choice