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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.



Directed Sets.
Comments

This is for upward directed sets; downward is analogous

Axioms

relation        R(2,infix)

variable        x,y,z

axiom              ∀x xRx                            #reflexive

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

axiom              ∀x∀y∃z zRx ⋀ zRy

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



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