The <Fn forcing> $\operatorname{Fn}(X,Y,\kappa)$ consists of partial functions $p:X\rightharpoonup Y$ such that
$$
|\operatorname{dom}p|<\kappa.
$$
It is ordered by reverse inclusion: $p\leq q$ exactly when $p\supseteq q$, so a stronger condition supplies more values.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 128 / 3 / a / ii / Solution

{c}
{title2=$\operatorname{Fn}(X,Y,\kappa)$}

The order $\operatorname{Fn}(X,Y,\kappa)$ consists of partial functions $p:X\rightharpoonup Y$ with $|\operatorname{dom}p|<\kappa$, ordered by reverse inclusion so that larger functions are stronger conditions.

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