For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

For the ancient Greek mathematicians, geometry was the crown jewel of their sciences, reaching a completeness and perfection of methodology that no other branch of their knowledge had attained.

For the sake of completeness, this article includes all edible aquatic life.

For example, Ibn Taymiyya took the position that since tafsir and sira-maghazi reports were commonly transmitted by incomplete isnads, these reports should not be assessed according to the completeness of the chains but rather on the basis of recurrent transmission of common meaning between reports.

For the sake of completeness they may be stated here.

For the sake of completeness, the set of all are also included as natural variables, although they are sometimes ignored.

For reasons stated in Anti-frogman techniques # Sending other frogmen against them, underwater fights between divers are much rarer in reality than in fiction, and thus suitability of the frogman's kit for " diver to diver combat " is less important than some other features when designing it ; but the point is considered here for completeness.

For example, the completeness of a linear order, which is used to characterize the real numbers as a complete ordered field, is a non-first-order property.

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 ).

For this reason, posets with certain completeness properties can often be described as algebraic structures of a certain kind.

# For completeness, compute the translational holonomy for loops in other hyperplanes, to prove that the other loops generate no affine torsion in the continuum limit.

For completeness, below are references to some speculative physical theories that employ torsion in ways that are different from Einstein – Cartan theory.

For completeness a so-called Stirling-type single-orifice PTR is represented schematically in Fig. 7.

For a side project, 4-Track Demos received remarkably high praise: Entertainment Weekly called it " a chillingly intimate peek into the fierce musical ethic of an independent and compelling voice ", Melody Maker hailed it as " viciously aggressive music with no numbing narcotic qualities ", while Rolling Stone said in its four-star review that " its depth, range and conceptual completeness make you wonder why Harvey even bothered with such conventions as a band or a producer in the first place ".

For completeness, this table includes champions from National League One ( 2003 – 2008 ) and the Co-operative Championship ( 2009-present )

For completeness, this table includes champions from National League Two ( 2003-2008 ) and the Championship 1 ( 2009-Present )

For completeness, this table includes the 1973 – 74 Club Championship, and premiership winners from the Super League era.

For completeness, Colson uses examples and describes addition ( pp 163, 4 ), multiplication ( pp 165, 6 ) and division ( pp 170, 1 ) using a table of multiples of the divisor.

For completeness, the inertial acceleration due to impressed external forces can be determined from the total physical force in the inertial ( non-rotating ) frame ( for example, force from physical interactions such as electromagnetic forces ) using Newton's second law in the inertial frame:

For example, electronic signatures are used not only when documents are sent, but also in data capture via scanning, in order to document the completeness of the capture.

; 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.

For completeness, he replaces Togusa's memories of his face with the Laughing Man logo, and wipes the memories of his friends ( who apparently not only consent to this treatment, but seem to expect it ).

For instance, IT application controls that ensure completeness of transactions can be directly related to financial assertions.

For example, the 14th Dalai Lama, long insistent on Tibet's history being separate from that of China's, conceded in 2005 that Tibet " is a part " of China's " 5000-year history " as part of a new proposal for Tibetan autonomy.

For a time, his classification considered bold and speculative, especially the proposal of a Nilo-Saharan languages family.

For example, in Canada, one proposal to reform the electoral system would see a 5 % national threshold, 1 % of the vote and 1 seat in the House of Commons, or 2 % nationally and 15 % of the vote in any one province.

For the NPC to formally defeat a proposal put before it is a rare, but not non-existent event.

For example, one possible proposed redefinition is " the ampere ... is such that the value of the elementary charge e ( charge on a proton ) is exactly 1. 602176487 × 10 < sup >− 19 </ sup > coulomb " This proposal is not yet accepted as part of the SI system: The SI definitions are unlikely to change until at least 2015.

For the simple Metropolis algorithm described here, this proposal density must be symmetric in that.

In his second proposal, the Indian warrior was replaced by a soldier holding a sword, and the motto was shortened to " Bello vel paci ", meaning " For war or for peace ".

For works written independently of the publisher, writers often first submit a query letter or proposal directly to a literary agent or to a publisher.

For this use, the military ensign would have a white field included with a golden marker: For the Harbour pilots ( as of 1881, based on a proposal of 1825 ) an anchor with a star ; for the Customs ( as of 1844 ) the letter " T " topped a royal crown ; for the Royal Mail ( as of 1844 ) a postal horn with a royal crown.

For example, Hakubun Shimomura gave " preserving that Y chromosome " as his reason for opposing a proposal to allow a future child of Princess Aiko to become Emperor one day, even if there were no grandsons of Emperor Akihito.

For example, empirical support has been obtained using analogy problem solving experiments for the proposal that midway through the creative process one's mind is in a potentiality state.

For their part, only a minority of Republican congressmen supported President George W. Bush's 2005 proposal to partially privatize Social Security, an idea strongly backed by the Institute.

For the definition of a specific bargaining solution it is usual to follow Nash's proposal, setting out the axioms this solution should satisfy.

Alaska has approximately half the known coal reserves in the U. S. For decades, there has been a proposal to build a large coal mine ( the Chuitna Coal Mine ) on the west side of Cook Inlet near the Chuitna River, and the native village of Tyonek, Alaska.

Pershing passed the proposal to Raymond Fosdick, who on giving it to Secretary of War Newton D. Baker promptly responded: " For God ’ s sake, Raymond, don ’ t show this to the president or he ’ ll stop the war.

For many distributions, finding a proposal distribution that includes the given distribution without a lot of wasted space is difficult.

For the April 2008 Constituent Assembly election, the party rejected the proposal of electoral alliance with the Communist Party of Nepal ( Maoist ), citing its own popularity among people, and it decided to compete in all constituencies.

For example, a code of alternative Belarusian orthography rules, based on the proposal of Vintsuk Vyachorka and published in 2005, has the optional letter ‹ ґ › included in the alphabet, but its use is not obligatory and in any case it can be replaced by ‹ г ›.

For example, in the 1970s, social psychologist L. Richard Hoffman noted that odds of a proposal's acceptance is strongly associated with the arithmetical difference between the number of utterances supporting versus rejecting that proposal.

In 2004 Microsoft merged their similar proposal, Caller-ID For Email, with SPF to form Sender ID Framework.

For some time, between 1961 and 1964, Chelomei's less aggressive proposal was accepted, and development of his UR-500 and the LK-1 were given a high priority.

For example, the 65th Battalion might have become 1st Battalion, City of Sydney's Own Regiment under one proposal or 1st Battalion, King George VI's Australian Rifle Regiment under another proposal.