In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset)...

of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness. Complete theories are closed under a number of conditions...

syntactic provability in first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the...

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...

particular completeness properties. Complete partial orders play a central role in theoretical computer science: in denotational semantics and domain theory. The...

up completeness, complete, completed, or incompleteness in Wiktionary, the free dictionary. Complete may refer to: Completeness (logic) Completeness of...

Syntactical completeness is a stronger property than semantic completeness. If a formal system is syntactically complete, a corresponding formal theory is called...

properties of the order topology to the completeness of X: If the order topology on X is connected, X is complete. X is connected under the order topology if...

and lower set Ideal and filter Ultrafilter Completeness (order theory) Dense order Distributivity (order theory) Modular lattice Distributive lattice Completely...

be the following overview articles: completeness properties of partial orders distributivity laws of order theory In the following, partial orders will...

The New World Order (NWO) is a term often used in conspiracy theories which hypothesize a secretly emerging totalitarian world government. The common...

generalized to the setting of partially ordered sets. See completeness (order theory). Dedekind completeness is the property that every Dedekind cut of the real...

additional assumptions, further conclusions may be possible; see Completeness (order theory) for more discussion of this subject. That article also discusses...

models of first-order theories. Gödel's completeness theorem, proved by Kurt Gödel in 1929, establishes that there are sound, complete, effective deductive...

the completeness theorem that the two meanings coincide. In other logics, such as second-order logic, there are syntactically consistent theories that...

all. By Gödel's completeness theorem, it is the only theory (for any given language) with no models. It is not the same as the theory of the empty set...

original Boolean algebra. Order theory knows many completion procedures to turn posets into posets with additional completeness properties. For example...

model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding. Equivalently, every first-order formula...

fact ( A , ≤ ) {\displaystyle (A,\leq )} is a complete lattice; for details, see completeness (order theory). If some power set ℘ ( X ) {\displaystyle \wp...

adequate. From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of...

closed upwards, and A contains no greatest element. See also completeness (order theory). It is straightforward to show that a Dedekind cut among the...

equivalent for any theory formulated in a particular deductive logic, the logic is called complete.[citation needed] The completeness of the propositional...

the Theory of NP-Completeness is a textbook by Michael Garey and David S. Johnson. It was the first book exclusively on the theory of NP-completeness and...

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...

empty set. Other properties may be assumed; see the article on completeness in order theory for more discussion on this subject. That article also discusses...

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other....

In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima...

expansions sometimes give good results, c.f. the exact solution, at lower order. In the theory of quantum electrodynamics (QED), in which the electron–photon interaction...

Bounded completeness has various relationships to other completeness properties, which are detailed in the article on completeness in order theory. The term...

was to produce axiomatic theories for all parts of mathematics, this limitation was particularly stark. Gödel's completeness theorem established the equivalence...