In[]:=
g=SimpleGraph[Catenate@Map[ax|->Catenate[Thread/@{AxiomaticTheory[ax,"Subtheories"]->ax,AxiomaticTheory[ax,"EquivalentTheories"]ax,ax->AxiomaticTheory[ax,"Supertheories"]}],AxiomaticTheory[]],VertexLabelsv_:>Placed[v,Tooltip]]
Out[]=
In[]:=
HighlightGraph[g,EdgeList[g,_UndirectedEdge]]
Out[]=
In[]:=
Dataset@AssociationMap[ax|->Column/@AssociationMap[AxiomaticTheory[ax,#]&,{"Subtheories","EquivalentTheories","Supertheories"}],AxiomaticTheory[]]
Out[]=
Subtheories
EquivalentTheories
Supertheories
AbelianGroupAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
RingAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
MeadowAxioms
FieldAxioms
AbelianMcCuneAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
RingAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
MeadowAxioms
FieldAxioms
AbelianTarskiAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianMcCuneAxioms
RingAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
MeadowAxioms
FieldAxioms
BooleanAxioms
​
HuntingtonAxioms
RobbinsAxioms
ShefferAxioms
HillmanAxioms
MeredithAxioms
OrNotBooleanAxioms
WolframAxioms
WolframAlternateAxioms
WolframCommutativeAxioms
​
CentralGroupoidAxioms
​
​
​
CombinatorAxioms
​
​
​
CommutativeRingAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
RingAxioms
RightNearRingAxioms
LeftNearRingAxioms
​
CommutativeRingWithIdentityAxioms
MeadowAxioms
FieldAxioms
CommutativeRingWithIdentityAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
RingAxioms
RightNearRingAxioms
LeftNearRingAxioms
​
MeadowAxioms
FieldAxioms
EquivalentialCalculusAxioms
​
​
GroupAxioms
FieldAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
RingAxioms
SemiringAxioms
RightNearRingAxioms
LeftNearRingAxioms
​
​
GroupAxioms
SemigroupAxioms
MonoidAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
RingAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
MeadowAxioms
FieldAxioms
RightNearRingAxioms
LeftNearRingAxioms
HigmanNeumannAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
RingAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
MeadowAxioms
FieldAxioms
RightNearRingAxioms
LeftNearRingAxioms
HillmanAxioms
​
BooleanAxioms
HuntingtonAxioms
MeredithAxioms
OrNotBooleanAxioms
RobbinsAxioms
ShefferAxioms
WolframAxioms
WolframAlternateAxioms
WolframCommutativeAxioms
​
HuntingtonAxioms
​
BooleanAxioms
RobbinsAxioms
ShefferAxioms
HillmanAxioms
MeredithAxioms
OrNotBooleanAxioms
WolframAxioms
WolframAlternateAxioms
WolframCommutativeAxioms
​
ImplicationalCalculusAxioms
​
​
​
JunctionalCalculusAxioms
​
​
​
LeftNearRingAxioms
SemigroupAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
​
CommutativeRingWithIdentityAxioms
RingWithIdentityAxioms
CommutativeRingAxioms
RingAxioms
FieldAxioms
MeadowAxioms
McCuneAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
RingAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
MeadowAxioms
FieldAxioms
RightNearRingAxioms
LeftNearRingAxioms
MeadowAxioms
SemigroupAxioms
MonoidAxioms
GroupAxioms
HigmanNeumannAxioms
McCuneAxioms
AbelianGroupAxioms
AbelianTarskiAxioms
AbelianMcCuneAxioms
CommutativeRingWithIdentityAxioms
CommutativeRingAxioms
RingWithIdentityAxioms
RingAxioms
SemiringAxioms
RightNearRingAxioms
LeftNearRingAxioms
​
​
MeredithAxioms
​
BooleanAxioms
HuntingtonAxioms
RobbinsAxioms
HillmanAxioms
OrNotBooleanAxioms
ShefferAxioms
WolframAxioms
WolframAlternateAxioms
WolframCommutativeAxioms
​
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