Abstract
For a set X with at least 3 elements, we establish a canonical one to one correspondence between all betweenness relations satisfying certain axioms and all pairs of inverse orderings “<” and “>” defined on X for which the corresponding Hasse diagram is connected and all maximal chains contain at least 3 elements. For an ordering “<”, the corresponding betweenness relation B is given by $$B=\{(x,y,z)\in X^3\mid x<y<z {\rm \ or\ }z<y<x\}.$$ Moreover, by adding one more axiom, we obtain also a one to one correspondence between all pairs of dual lattices and all betweenness relations.
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