Indicwiki: 1 revision imported from :alpha:Template:Pointclasses

2023-02-08T13:28:12Z

1 revision imported from alpha:Template:Pointclasses

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alpha>Indicwiki: Created page with "{{navbar|Pointclasses}} {| class="wikitable" style="text-align: center;" |- !colspan=2| {{nobold|Lightface}} !colspan=2| Boldface hierarchy|Boldface..."

2023-01-27T20:09:08Z

Created page with "{{navbar|Pointclasses}} {| class="wikitable" style="text-align: center;" |- !colspan=2| {{nobold|Lightface}} !colspan=2| Boldface hierarchy|Boldface..."

New page

{{navbar|Pointclasses}}
{| class="wikitable" style="text-align: center;"
|-
!colspan=2| {{nobold|[[Lightface hierarchy|Lightface]]}}
!colspan=2| [[Boldface hierarchy|Boldface]]
|-
|colspan=2|Σ{{su|p=0|b=0}} = Π{{su|p=0|b=0}} = Δ{{su|p=0|b=0}} (sometimes the same as Δ{{su|p=0|b=1}})
|colspan=2|'''Σ{{su|p=0|b=0}}''' = '''Π{{su|p=0|b=0}}''' = '''Δ{{su|p=0|b=0}}''' (if defined)
|-
|colspan=2|Δ{{su|p=0|b=1}} = [[computable set|recursive]]
|colspan=2|'''Δ{{su|p=0|b=1}}''' = [[clopen set|clopen]]
|-
|Σ{{su|p=0|b=1}} = [[Computably enumerable set|recursively enumerable]]
|Π{{su|p=0|b=1}} = co-recursively enumerable
|'''Σ{{su|p=0|b=1}}''' = ''G'' = [[open set|open]]
|'''Π{{su|p=0|b=1}}''' = ''F'' = [[closed set|closed]]
|-
|colspan=2| Δ{{su|p=0|b=2}}
|colspan=2| '''Δ{{su|p=0|b=2}}'''
|-
|Σ{{su|p=0|b=2}}
|Π{{su|p=0|b=2}}
|'''Σ{{su|p=0|b=2}}''' = [[Fσ set|''F''σ]]
|'''Π{{su|p=0|b=2}}''' = [[Gδ set|''G''δ]]
|-
|colspan=2| Δ{{su|p=0|b=3}}
|colspan=2| '''Δ{{su|p=0|b=3}}'''
|-
|Σ{{su|p=0|b=3}}
|Π{{su|p=0|b=3}}
|'''Σ{{su|p=0|b=3}}''' = ''G''δσ
|'''Π{{su|p=0|b=3}}''' = ''F''σδ
|-
|colspan=2|⋮
|colspan=2|⋮
|-
|colspan=2|Σ{{su|p=0|b=<ω}} = Π{{su|p=0|b=<ω}} = Δ{{su|p=0|b=<ω}} = Σ{{su|p=1|b=0}} = Π{{su|p=1|b=0}} = Δ{{su|p=1|b=0}} = [[arithmetical set|arithmetical]]
|colspan=2|'''Σ{{su|p=0|b=<ω}}''' = '''Π{{su|p=0|b=<ω}}''' = '''Δ{{su|p=0|b=<ω}}''' = '''Σ{{su|p=1|b=0}}''' = '''Π{{su|p=1|b=0}}''' = ''' Δ{{su|p=1|b=0}}''' = boldface arithmetical
|-
|colspan=2|⋮
|colspan=2|⋮
|-
|colspan=2| Δ{{su|p=0|b=α}} (α [[recursive ordinal|recursive]])
|colspan=2| '''Δ{{su|p=0|b=α}}''' (α [[countable ordinal|countable]])
|-
|Σ{{su|p=0|b=α}}
|Π{{su|p=0|b=α}}
|'''Σ{{su|p=0|b=α}}'''
|'''Π{{su|p=0|b=α}}'''
|-
|colspan=2|⋮
|colspan=2|⋮
|-
|colspan=2| Σ{{su|p=0|b=[[Church–Kleene ordinal|ω{{su|p=CK|b=1}}]]}} = Π{{su|p=0|b=ω{{su|p=CK|b=1}}}} = Δ{{su|p=0|b=ω{{su|p=CK|b=1}}}} = Δ{{su|p=1|b=1}} = [[Hyperarithmetical theory|hyperarithmetical]]
|colspan=2| '''Σ{{su|p=0|b=[[First uncountable ordinal|ω1]]}}''' = '''Π{{su|p=0|b=ω1}}''' = '''Δ{{su|p=0|b=ω1}}''' = '''Δ{{su|p=1|b=1}}''' = '''B''' = [[Borel set|Borel]]
|-
|Σ{{su|p=1|b=1}} = lightface analytic
|Π{{su|p=1|b=1}} = lightface coanalytic
|'''Σ{{su|p=1|b=1}}''' = A = [[analytic set|analytic]]
|'''Π{{su|p=1|b=1}}''' = CA = [[coanalytic set|coanalytic]]
|-
|colspan=2| Δ{{su|p=1|b=2}}
|colspan=2| '''Δ{{su|p=1|b=2}}'''
|-
|Σ{{su|p=1|b=2}}
|Π{{su|p=1|b=2}}
|'''Σ{{su|p=1|b=2}}''' = PCA
|'''Π{{su|p=1|b=2}}''' = CPCA
|-
|colspan=2| Δ{{su|p=1|b=3}}
|colspan=2| '''Δ{{su|p=1|b=3}}'''
|-
|Σ{{su|p=1|b=3}}
|Π{{su|p=1|b=3}}
|'''Σ{{su|p=1|b=3}}''' = PCPCA
|'''Π{{su|p=1|b=3}}''' = CPCPCA
|-
|colspan=2|⋮
|colspan=2|⋮
|-
|colspan=2|Σ{{su|p=1|b=<ω}} = Π{{su|p=1|b=<ω}} = Δ{{su|p=1|b=<ω}} = Σ{{su|p=2|b=0}} = Π{{su|p=2|b=0}} = Δ{{su|p=2|b=0}} = [[analytical hierarchy|analytical]]
|colspan=2|'''Σ{{su|p=1|b=<ω}}''' = '''Π{{su|p=1|b=<ω}}''' = '''Δ{{su|p=1|b=<ω}}''' = '''Σ{{su|p=2|b=0}}''' = '''Π{{su|p=2|b=0}}''' = ''' Δ{{su|p=2|b=0}}''' = '''P''' = [[projective hierarchy|projective]]
|-
|colspan=2|⋮
|colspan=2|⋮
|}
<noinclude>[[Category:Mathematics navigational boxes]]</noinclude>

Template:Pointclasses - Revision history

Indicwiki: 1 revision imported from :alpha:Template:Pointclasses

alpha>Indicwiki: Created page with "{{navbar|Pointclasses}} {| class="wikitable" style="text-align: center;" |- !colspan=2| {{nobold|Lightface}} !colspan=2| Boldface hierarchy|Boldface..."