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Order theory

Antichain
Subset of incomparable elements
Antisymmetric relation
Binary relation such that if A is related to B and is different from it then B is not related to A
Boolean algebra (structure)
Algebraic structure modeling logical operations
Comparability
Mathematical relation with respect to a partial order
Connected relation
Binary endorelation such that for every pair of elements either first is related with second or second is related with first
Covering relation
Mathematical relation inside orderings
Domain theory
Branch of mathematics relating to posets
Duality (order theory)
Term in the mathematical area of order theory
Filter (mathematics)
In mathematics, a special subset of a partially ordered set
Gale–Shapley algorithm
Algorithm for solving the stable matching problem
Greatest element and least element
An element of a preordered set that is ≥ (respectively, ≤) to all other elements (in contrast, it is maximal if it is the only element ≥ to itself)
Hasse diagram
Visual depiction of a partially ordered set
Ideal (order theory)
In order theory, a nonempty, upward‐directed, downward‐closed subset of a preordered set
Infimum and supremum
Greatest lower bound and least upper bound
Join and meet
Two related operations on a poset in order theory
Lattice (order)
Set whose pairs have minima and maxima
Order theory
Branch of mathematics
Partially ordered set
Mathematical set with an ordering
Preorder
Reflexive and transitive binary relation
Stable matching problem
Pairing where no unchosen pair prefers each other over their choice
Stable roommates problem
Mathematical problem of finding a stable matching for an even-sized set
Total order
Mathematical ordering where all elements can be compared
Ultrafilter
Maximal proper filter
Upper and lower bounds
Majorant and minorant in mathematics
Well-founded relation
Type of binary relation
Well-order
Class of mathematical orderings