Schama mooted some possible ( invented ) connections between the two cases, exploring the historian's inability " ever to reconstruct a dead world in its completeness however thorough or revealing the documentation ," and speculatively bridging " the teasing gap separating a lived event and its subsequent narration.

Another interesting way to characterize completeness properties is provided through the concept of ( monotone ) Galois connections, i. e. adjunctions between partial orders.

In fact this approach offers additional insights both in the nature of many completeness properties and in the importance of Galois connections for order theory.

The general observation on which this reformulation of completeness is based is that the construction of certain suprema or infima provides left or right adjoint parts of suitable Galois connections.

USNO-B1. 0 is believed to provide all-sky coverage, completeness down to V = 21, 0. 2 arcsecond astrometric accuracy at J2000. 0, 0. 3 magnitude photometric accuracy in up to five colors, and 85 % accuracy for distinguishing stars from non-stellar objects.

OWL DL was designed to provide the maximum expressiveness possible while retaining computational completeness ( either φ or ¬ φ belong ), decidability ( there is an effective procedure to determine whether φ is derivable or not ), and the availability of practical reasoning algorithms.

The former provide a general equilibrium model to explain a small liquidity preference shock in one region can spread by contagion throughout the economy and the possibility of contagion depends strongly on the completeness of the structure of interregional claims.

While eschewing completeness ( in the range of variants and in the citation of witnesses ), this edition does provide informed readers with a basis by which they can judge for themselves which readings more accurately reflect the originals.

** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.

In contrast, other, more systematic algorithms achieved, at least theoretically, completeness for first-order logic.

Since Cauchy sequences can also be defined in general topological groups, an alternative to relying on a metric structure for defining completeness and constructing the completion of a space is to use a group structure.

By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced from the axioms, so the can also be viewed as asking for an algorithm to decide whether a given statement is provable from the axioms using the rules of logic.

In August 1970, Gödel told Oskar Morgenstern that he was " satisfied " with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödel would not publish because he was afraid that others might think " that he actually believes in God, whereas he is only engaged in a logical investigation ( that is, in showing that such a proof with classical assumptions ( completeness, etc.

A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense.

Thus, in a sense, there is a different completeness theorem for each deductive system.

The name for the incompleteness theorem refers to another meaning of complete ( see model theory-Using the compactness and completeness theorems ).

Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem.

Weak König's lemma is provable in ZF, the system of Zermelo – Fraenkel set theory without axiom of choice, and thus the completeness and compactness theorems for countable languages are provable in ZF.

The completeness theorem is a central property of first-order logic that does not hold for all logics.

Second-order logic, for example, does not have a completeness theorem for its standard semantics ( but does have the completeness property for Henkin semantics ), and the same is true of all higher-order logics.

A completeness theorem can be proved for modal logic or intuitionistic logic with respect to Kripke semantics.

The reason for that is the completeness of propositional logic, with the existential quantifiers playing no role.

The Department of Safeguards is responsible for carrying out this mission, through technical measures designed to verify the correctness and completeness of states ' nuclear declarations.

Where Hegel argues that an ultimate understanding of the logical structure of the world is an understanding of the logical structure of God's mind, Kierkegaard asserting that for God reality can be a system but it cannot be so for any human individual because both reality and humans are incomplete and all philosophical systems imply completeness.

His study of Tagalog has been described as “… the best treatment of any Austronesian language … The result is a description of Tagalog which has never been surpassed for completeness, accuracy, and wealth of exemplification .”

The murals displayed the image of the Balhae people in its completeness for the first time.

For the sake of completeness, Swedish forms often ask people to fill in all their given names and to indicate which one is their " name of address " ( tilltalsnamn ).

The murals displayed the image of the Balhae people in its completeness.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

The completeness theorem says that if a formula is logically valid then there is a finite deduction ( a formal proof ) of the formula.

* whether there exists a mathematical statement which could neither be proven nor disproven in the system ( the question of completeness ).

# The state that exists when there is complete assurance that under all conditions an IT system is based on the logical correctness and reliability of the operating system, the logical completeness of the hardware and software that implement the protection mechanisms, and data integrity.

In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals ( or some other equivalent formulation of completeness ), which is not an algebraic concept.

In theories of arithmetic, such as Peano arithmetic, there is an intricate relationship between the consistency of the theory and its completeness.

Although there is no record of Einstein responding to Born and Heisenberg during the technical sessions of the Fifth Solvay Congress, he did challenge the completeness of quantum mechanics during informal discussions over meals, presenting a thought experiment intended to demonstrate that quantum mechanics could not be entirely correct.

Therefore, when the completeness axiom is added, it can be proved that any two models must be isomorphic, and so in this sense, there is only one complete ordered Archimedean field.

) However, there are some general patterns, and for reasons of space and completeness this article deals mainly with the largest organizations on a country-by-country basis.

To avoid transfinite induction, and to make directed completeness equivalent to ω-completeness, it is convenient to assume also that there are only countably many isolated elements which motivates the following definition.

The difficulty is in effective computation of bounds: for a given discriminant, it is easy to compute the class number, and there are several ineffective lower bounds on class number ( meaning that they involve a constant that is not computed ), but effective bounds ( and explicit proofs of completeness of lists ) are harder.

; completeness: For every n-ary operator of A, there exists an n-ary operator of B such that

; completeness: For every term of language A and every terms of language B, if then there exists some such that.

; completeness: for every observable on terms of A, there exists an observable on terms of B such that for any term with observable, has observable.

# If the formula is valid, then by completeness of cut-free sequent calculus, which follows from Gentzen's cut-elimination theorem, there is a cut-free proof of.

* independently proved the completeness, and showed that if the definition of uniform polyhedron is relaxed to allow edges to coincide then there is just one extra possibility.