An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value, optimization (mathematics), domain theory.

Table of contents

1 Partial orders 2 In abstract algebra 3 In mathematical logic 4 Directed set

Partial orders

• Hasse diagram
• Monotonic
• Preorder
• Total order
  • Total preorder
  • Chain
• Well-order
  • Well-founded relation
  • Ordinal number
  • Well partial order
• Least upper bound
  • Greatest lower bound
  • Limit superior and limit inferior
  • Extended real number line
• Antichain
• Cofinality
• Dense
• Dedekind completion
• Infinite descending chain
  • Ascending chain condition
• Lattice
  • Knaster-Tarski theorem
• Boolean algebra
  • Boolean ring
  • Kleene algebra
• Heyting algebra
  • Pointless topology
• Galois connection
  • Closure operator
• Relative complement
• Incidence algebra

• Ordered group
  • Archimedean property
• Ordered field
• Artinian
• Noetherian
• Linearly ordered group

• Zorn's lemma
  • Hausdorff maximality theorem
• Boolean prime ideal theorem
• Suslin's problem