{"id":"palomar/PALOMAR-2026-11-01-000001","url":"https://github.com/konrad-012/no-universal-fsigma/tree/310d90d3553ccf01c4e7276262df6d687db82bb7","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-01-000001-v1.json","repo":"https://github.com/konrad-012/no-universal-fsigma","tags":["math.LO","msc:03E15"],"score":0,"title":"There is no universal Fσ equivalence relation","trust":"high","domain":"math.LO","source":"palomar","authors":["Konrad Deka"],"reviews":0,"subject":"math.LO","summary":"There is no universal Fσ equivalence relation. This is the main result of arxiv:2610.31052. More detail: An equivalence relation E on a Polish space X is said to be Fσ if it is a countable union of closed subsets of X × X. For equivalence relations E and F on Polish spaces X and Y, we say that E is Borel reducible to F, written E ≤_B F, if there exists a Borel function f : X → Y such that for all x, y ∈ X, we have x E y if and only if f(x) F f(y). An Fσ equivalence relation E is universal if for every Fσ equivalence relation F, we have F ≤_B E. The theorem states that there's no such relation.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-01","reactions":{},"formalized":true,"formalizes":[{"title":"There is no universal Fσ equivalence relation","identifier":"https://arxiv.org/abs/2610.31052v1","relationship":"formalizes"}]}