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Online Encyclopedia of
Mathematical Models.






Models:

boolean algebras, lattices, directed sets, equivalence relations,
graphs, directed graphs, bipartite graphs,
pre-orderings, strict partial orders, strict weak orderings, partial orderings, weak orderings, total orderings,
groups, rings, fields, racks, quandles, Tarski's HS Algebra,
more coming soon.



Quandles.
Axioms

relation =(2,infix) {a0==a1}

function ⊲(2,infix)

variable x,y,z,w

axiom ∀x x⊲x=x

axiom ∀x∀y∀z x⊲(y⊲z)=(x⊲y)⊲(x⊲z) #self-distributive law

axiom ∀x∀y∃z x⊲z=y ⋀ ∀w x⊲w=y ⟶ z=w

Comments

Racks with the axiom: ∀x x⊲x=x.

Models
model 1_1
 ⊲
   0
model 2_1
 ⊲
   0 1
   0 1
model 3_1
 ⊲
   0 2 1
   2 1 0
   1 0 2
model 3_2
 ⊲
   0 1 2
   0 1 2
   1 0 2
model 3_3
 ⊲
   0 1 2
   2 1 0
   0 1 2
model 3_4
 ⊲
   0 2 1
   0 1 2
   0 1 2
model 3_5
 ⊲
   0 1 2
   0 1 2
   0 1 2



      



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