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