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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.



Pre-Orderings. (``Quasi-Orderings.'')
Axioms

relation        R(2,infix)

variable        x,y,z

axiom              ∀x xRx                            #reflexive

axiom              ∀x∀y∀z ((xRy ⋀ yRz) ⟶ xRz)       #transitive

Models
model 1_1
 R
   1
model 2_1
 R
   1 0
   0 1
model 2_2
 R
   1 1
   0 1
model 2_3
 R
   1 0
   1 1
model 2_4
 R
   1 1
   1 1
model 3_1
 R
   1 0 0
   0 1 0
   0 0 1
model 3_2
 R
   1 1 0
   0 1 0
   0 0 1
      



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