# descriptive set theory – Universal Set for $\mathcal{A}\Pi^1_1$ Answer

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## descriptive set theory – Universal Set for $\mathcal{A}\Pi^1_1$

I’m probably missing something easy but I’m having trouble with the first part of Kechris’s Classical Descriptive Set Theory, Exercise 29.17, the first part:

For an uncountable Polish space $$Y$$show that there is a $$Y$$-universal set for $$\mathcal{A}\Pi^1_1$$where $$\mathcal{A}$$ is the Souslin operator.

I know wlog we can take $$Y = \mathbb{N}^\mathbb{N}$$ and then we have easy examples of $$\mathbb{N}^\mathbb{N}$$-universal sets for $$\Pi^1_1$$but I can’t seem to make the leap to $$\mathcal{A}\Pi^1_1$$.

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