Template:Pointclasses
From Vigyanwiki
Lightface | Boldface | ||
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Σ0 0 = Π0 0 = Δ0 0 (sometimes the same as Δ0 1) |
Σ0 0 = Π0 0 = Δ0 0 (if defined) | ||
Δ0 1 = recursive |
Δ0 1 = clopen | ||
Σ0 1 = recursively enumerable |
Π0 1 = co-recursively enumerable |
Σ0 1 = G = open |
Π0 1 = F = closed |
Δ0 2 |
Δ0 2 | ||
Σ0 2 |
Π0 2 |
Σ0 2 = Fσ |
Π0 2 = Gδ |
Δ0 3 |
Δ0 3 | ||
Σ0 3 |
Π0 3 |
Σ0 3 = Gδσ |
Π0 3 = Fσδ |
⋮ | ⋮ | ||
Σ0 <ω = Π0 <ω = Δ0 <ω = Σ1 0 = Π1 0 = Δ1 0 = arithmetical |
Σ0 <ω = Π0 <ω = Δ0 <ω = Σ1 0 = Π1 0 = Δ1 0 = boldface arithmetical | ||
⋮ | ⋮ | ||
Δ0 α (α recursive) |
Δ0 α (α countable) | ||
Σ0 α |
Π0 α |
Σ0 α |
Π0 α |
⋮ | ⋮ | ||
Σ0 ωCK 1 = Π0 ωCK 1 = Δ0 ωCK 1 = Δ1 1 = hyperarithmetical |
Σ0 ω1 = Π0 ω1 = Δ0 ω1 = Δ1 1 = B = Borel | ||
Σ1 1 = lightface analytic |
Π1 1 = lightface coanalytic |
Σ1 1 = A = analytic |
Π1 1 = CA = coanalytic |
Δ1 2 |
Δ1 2 | ||
Σ1 2 |
Π1 2 |
Σ1 2 = PCA |
Π1 2 = CPCA |
Δ1 3 |
Δ1 3 | ||
Σ1 3 |
Π1 3 |
Σ1 3 = PCPCA |
Π1 3 = CPCPCA |
⋮ | ⋮ | ||
Σ1 <ω = Π1 <ω = Δ1 <ω = Σ2 0 = Π2 0 = Δ2 0 = analytical |
Σ1 <ω = Π1 <ω = Δ1 <ω = Σ2 0 = Π2 0 = Δ2 0 = P = projective | ||
⋮ | ⋮ |