List of order structures in mathematics
https://en.wikipedia.org/wiki/List_of_order_structures_in_mathematics
In mathematics, and more specifically in order theory, several different types of ordered set have been studied. They include:
Cyclic order, orderings in which triples of elements are either clockwise or counterclockwise
Lattice, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types of lattice have been studied; see map of lattices for a list.
Partially ordered set (poset), orderings in which some pairs are comparable and others might not be
Preorder, a generalization of partial orders allowing ties (represented as equivalences and distinct from incomparabilities)
Semiorder, partial orders determined by comparison of numerical values, in which values that are too close to each other are incomparable; a subfamily of partial orders with certain restrictions
Total order, orderings that specify, for every two distinct elements, which one is less than the other. that is, all elements are comparable.
Weak order, generalization of total order allowing ties (represented either as equivalence or, in strict weak orders, as transitive incomparability)
Well-order, total order in which every non-empty subset has an infinum
Well-quasi-ordering, a class of preorders generalizing the well-orders
Refs
List of order theory topics Glossary of order theory Categories Mathematics-related lists Order theory
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