It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

An important consequence of the KAM theorem is that for a large set of initial conditions the motion remains perpetually quasiperiodic.

As a consequence of the initial competing claims of discovery, an element naming controversy arose.

In consequence, Army forces deploying to Africa suffered serious initial reverses when encountering German armored combat units in Africa at Kasserine Pass and other major battles.

One consequence of this is that unlike helium-4, the amount of deuterium is very sensitive to initial conditions.

One performance issue is the 1 / 2 factor in the initial value of D. Since all of this is about the sign of the accumulated difference, then everything can be multiplied by 2 with no consequence.

Concomitant esotropias can arise as an initial problem, in which case they are designated as ' Primary ', as a consequence of loss or impairment of vision, in which case they are designated as ' Secondary ', or following overcorrection of an initial Exotropia in which case they are described as being ' Consecutive '.

Because of the high initial investments, many less wealthy nations cannot afford to develop or sustain appropriate infrastructure, and as a consequence people in these areas may spend a correspondingly higher fraction of their income on water.

The thermodynamic arrow of time and the Second law of thermodynamics are thought to be a consequence of the initial conditions in the early universe.

A simple consequence of the fluctuation theorem given above is that if we carry out an arbitrarily large ensemble of experiments from some initial time t = 0, and perform an ensemble average of time averages of the entropy production then an exact consequence of the FT is that the ensemble average cannot be negative for any value of the averaging time t:

After initial success, the attack had to be broken off in consequence of the danger posed to the Russian front following the Brussilow offensive of June 1916 and the subsequent transfer of formations to that threatened front.

A demonstration consists of a sequence of steps, each step justified by an initial or a previously demonstrated consequence.

According to Coleman, it is none other than the Congress itself — if and when the Congress should later be presented with valid ratifications from the required number of states — which has the discretion to arbitrate the question of whether too much time has elapsed between Congress ' initial proposal of that amendment and the most recent state ratification thereof assuming that, as a consequence of that most recent ratification, the legislatures of ( or conventions conducted within ) at least three-fourths of the states have ratified that amendment at one time or another.

A consequence of this potential energy function is that it is possible to shift the initial position of an electron by any lattice vector without changing any aspect of the problem, thereby defining a discrete symmetry.

Flood basalt provinces may also occur as a consequence of the initial hot-spot activity in ocean basins as well as on continents.

After the complexities under the " but for " test have been addressed, the courts may still deny compensation if the harm was a very remote consequence of the initial wrong.

Lesk concludes that the parameterization that Moseley discovered, and that he ' incorrectly ' interpreted in terms of the Bohr theory of hydrogen, is actually, predominantly a consequence of the difference of the value of the electron-electron repulsion in the initial and final states of the atom that undergoes the x-ray transition.

In 1948, as a consequence of their studies of nucleosynthesis in the early expanding Big Bang universe model, they made the first theoretical prediction of the existence of a residual, homogeneous, isotopic, blackbody radiation ( cosmic microwave background radiation ) that pervades the universe as a vestige of the initial Big Bang explosion.

As a consequence, small organisms must have higher specific metabolic rates to combat this loss of energy over their large surface area to volume ratio.

Areas of focus: maritime domain awareness ; combat system interoperability ; fleet systems ; command-and-control structures: precision strike warfare ; consequence management ; counter-IED and counter-mining ; aircrew training ; engagement and humanitarian assistance operations ; and training for operators at the tactical and operational levels of war

One consequence was that the original combat graphics had been captured from the waist up only, as Michael Quarles had reasoned one must be close to a monster to fight it.

When a transferrin protein loaded with iron encounters a transferrin receptor on the surface of a cell ( e. g., to erythroid precursors in the bone marrow ), it binds to it and, as a consequence, is transported into the cell in a vesicle by receptor-mediated endocytosis.

`` This was not merely alleging errors, but was carried out by day-after-day allegations in memos, written charges of serious consequence.

The two Governments agree that the rupees accruing to the Government of the United States of America as a consequence of sales made pursuant to this Agreement will be used by the Government of the United States of America, in such manner and order of priority as the Government of the United States of America shall determine, for the following purposes in the amounts shown: ( A )

Existence is created and willed by God and is not the consequence of a pre-existent rebellion or of a cosmic descent from eternity into history.

We should not allow the image of an immanent end brought about indirectly by our own action in the continuing human struggle for a just endurable order of existence to blind us to the fact that in some measure accelerating the end of our lease may be one consequence among others of many other of mankind's thrusts toward we know not what future.

A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time ; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926.

As a consequence there are four chimney-pieces by Algardi in the Royal Palace of Aranjuez, and in the gardens, the figures on the fountain of Neptune are also by him.

He was such a favourite with the latter, that, when Greece was visited by a drought in consequence of a murder which had been committed, the oracle of Delphi declared that the calamity would not cease unless Aeacus prayed to the gods that it might.

Pomponius Mela mentions it among the small towns of the district, probably as it was eclipsed by its neighbour Tarraco ( modern Tarragona ), but it may be gathered from later writers that it gradually grew in wealth and consequence, favoured as it was with a beautiful situation and an excellent harbour.

However, documents released by the Cameroonians, in parity with that of the British and Germans, clearly places Bakassi under Cameroonian Territory as a consequence of colonial era Anglo-German agreements.

The surface of the water becomes slightly concave, with the consequence that the potential energy of the water at the greater radius is increased by the work done against gravity to achieve the greater height.

Bézout's lemma is a consequence of the Euclidean division defining property, namely that the division by a nonzero integer b has a remainder strictly less than | b |.

One consequence of this is that in standard general relativity, the universe began with a singularity, as demonstrated by Stephen Hawking and Roger Penrose in the 1960s.

A crime may be illegal ( as is the cause of evil or injury ) or perfectly legal ( when the act done is not a necessary consequence of the conduct of the agent but determined by others ).

As a consequence of the third point, if a and b are coprime and br ≡ bs ( mod a ), then r ≡ s ( mod a ) ( because we may " divide by b " when working modulo a ).

Block structure was introduced into computer programming languages by the Algol project ( 1957 – 1960 ), which, as a consequence, also featured a context-free grammar to describe the resulting Algol syntax.

As a consequence, in particular, in the system of coordinates given by the polar representation, the equations then take the form

As a consequence of oppression, forced labor, hunger, disease, and mass killings, by 1535, only 60, 000 were still alive.

That a rational number must have a finite or recurring decimal expansion can be seen to be a consequence of the long division algorithm, in that there are only q-1 possible nonzero remainders on division by q, so that the recurring pattern will have a period less than q.

Vancouver wrote of Whidbey's efforts: " This determined shore they had been exploring to be an island, which, in consequence of Mr. Whidbey ’ s circumnavigation, I distinguished by the name of Whidbey ’ s Island: and this northern pass, leading into Bay, Deception Passage ".

As a consequence, Domitian was popular with the people and army but considered a tyrant by members of the Roman Senate.

As a consequence, the anti-Domitianic tradition was already well established by the end of the 2nd century, and by the 3rd century, even expanded upon by early Church historians, who identified Domitian as an early persecutor of Christians.

In consequence of the accusation of Claudia Pulchra, and of some offense which he had given to Caligula, he was accused by the emperor in the senate, but by concealing his own skill in speaking, and pretending to be overpowered by the eloquence of Caligula, he not only escaped the danger, but was made consul suffectus in 39 AD.