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Terms in this set (38)
Reflexive
Vw(wRw)
Irreflexive
Vw(w!Rw)
Coreflexive
VwVv(wRv -> w=v)
Transitive
VwVvVu(wRv ^ vRu -> wRu)
Euclidian
VwVvVu(wRv ^ wRu -> vRu)
Dense
VwVv(wRv -> Eu(wRu ^ uRv))
Symmetric
VwVv(wRv -> vRw)
asymmetric
VwVv(wRv -> v!Rw)
antisymmetric
VwVv(wRv ^ vRw -> w=v)
serial
VwEv(wRv)
Inverse serial
VwEv(vRw)
universal
VwVv(wRv)
totally disconnected
VwVv(w!Rv)
connected
VwVv(wRv V vRw)
semi-connected
VwVv(w!=v -> wRv V vRw)
Piecewise connected
VwVvVu((uRw ^ uRv) -> (wRv V vRw))
convergent
VwVvVu(wRv ^ wRu -> Ez(vRz ^ uRz))
deterministic
VwVvVu(wRv ^ wRu -> v=u)
preordered
reflexive & transitive
equivalence
reflexive & transitive & symmetric
partially ordered
reflexive & transitive & antisymmetric
totally ordered
reflexive & transitive & antisymmetric & connected
reflexive frame
B phi -> phi
coreflexive frame
D phi -> phi
transitive frame
B phi -> BB phi
Dense frame
D phi -> DD phi
Serial frame
B phi -> D phi
Deterministic frame
D phi -> B phi
Symmetric frame
phi -> BD phi
Euclidian frame
D phi -> BD phi
Convergent frame
DB phi -> BD phi
Totally disconnected
B phi
Axiom K
B(phi -> psi) -> (B phi -> B psi)
Axiom T
B A -> A
Axiom B
A -> BD A
Axiom D
B A -> D A
Axiom 4
B A -> BB A
Axiom 5
D A -> BD A
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