A note on an effective Polish topology and Silver's Dichotomy theorem

Ramez L. Sami

英文摘要：

We define a Polish topology inspired from the Gandy-Harrington topology and show how it can be used to prove Silver's dichotomy theorem while remaining in the Polish realm. In this topology, a $Π^1_1$ equivalence relation decomposes into a "sum" of a clopen relation and a meager one. We characterize it as the largest regular toplogy with a basis included in $Σ^1_1$.

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