English

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

Logic 2019-08-27 v1 General Topology

Abstract

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 Π11\Pi^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 Σ11\Sigma^1_1.

Cite

@article{arxiv.1908.09214,
  title  = {A note on an effective Polish topology and Silver's Dichotomy theorem},
  author = {Ramez L. Sami},
  journal= {arXiv preprint arXiv:1908.09214},
  year   = {2019}
}
R2 v1 2026-06-23T10:55:58.650Z