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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.



Strict Partial Orderings
Axioms

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

relation ≤(2,infix)

variable x,y,z

axiom       ∀x ¬ x≤x              #irreflexive

axiom       ∀x∀y x≤y → ¬ y≤x       #asymmetric

axiom       ∀x∀y∀z x≤y ⋀ y≤z ⟶ x≤z       #transitive

Models
model 1_1
 ≤
   0
model 2_1
 ≤
   0 0
   0 0
model 2_2
 ≤
   0 1
   0 0
model 2_3
 ≤
   0 0
   1 0
model 3_1
 ≤
   0 0 0
   0 0 0
   0 0 0
model 3_2
 ≤
   0 1 0
   0 0 0
   0 0 0
model 3_3
 ≤
   0 0 1
   0 0 0
   0 0 0
      



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