# Order Theory

Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary.

### Other articles related to "order theory, theory, orders, order":

Theory (mathematical Logic) - First-order Theories - Interpretation of A First Order Theory
... An interpretation of a first-order theory provides a semantics for the formulas of the theory ... A model of a first order theory is an interpretation in which every formula of is satisfied ...
Order Theory - Related Mathematical Areas - Category Theory
... The visualization of orders with Hasse diagrams has a straightforward generalization instead of displaying lesser elements below greater ones, the direction of the ... In this way, each order is seen to be equivalent to a directed acyclic graph, where the nodes are the elements of the poset and there is a directed ... Functions between orders become functors between categories ...
Conservativity Theorem
... states the following Suppose that a closed formula is a theorem of a first-order theory ... Let be a theory obtained from by extending its language with new constants and adding a new axiom ... Then is a conservative extension of, which means that the theory has the same set of theorems in the original language (i.e ...
List Of PSPACE-complete Problems - Logic
... Quantified boolean formulas · First-order logic of equality · Satisfaction in intuitionistic propositional logic · Satisfaction in modal logic S4 · First-order theory of the natural numbers under the ...
Duality (order Theory)
... In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd ... This dual order Pop is defined to be the set with the inverse order, i.e ... if one poset is order isomorphic to the dual of the other ...

### Famous quotes containing the words theory and/or order:

Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.
Willard Van Orman Quine (b. 1908)

The worth of a State, in the long run, is the worth of the individuals composing it ... a State which dwarfs its men, in order that they may be more docile instruments in its hands even for beneficial purposes—will find that with small men no great thing can really be accomplished.
John Stuart Mill (1806–1873)