A real number a is first-order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ ( a ) holds in the standard model of set theory ( see Kunen 1980: 153 ).

This argument is embodied in the Copernican principle, which states that the Earth does not occupy a unique position in the Universe, and the mediocrity principle, which holds that there is nothing special about life on Earth.

Critical scholarship generally holds to the two-source hypothesis as most probable, which argues that the author used the Gospel of Mark and the hypothetical Q document in addition to unique material, as sources for the gospel.

**** Divine command theory holds that for a thing to be right is for a unique being, God, to approve of it, and that what is right for non-God beings is obedience to the divine will.

The unique form of sport portrayed is fundamentally based on classical and " catch " wrestling, with modern additions of striking attacks, strength-based holds and throws, and acrobatic maneuvers ; much of these derive from the influence of various international martial arts.

Principal ideal domains are thus mathematical objects which behave somewhat like the integers, with respect to divisibility: any element of a PID has a unique decomposition into prime elements ( so an analogue of the fundamental theorem of arithmetic holds ); any two elements of a PID have a greatest common divisor ( although it may not be possible to find it using the Euclidean algorithm ).

" The conclusion that Merge falls within UG holds whether such recursive generation is unique to FL or is

The Feld Hell Club holds monthly contests and gives out awards for hams who make contacts using this unique mode of communication.

Newman proved in 1976 the existence of a constant Λ for which the " if and only if " claim holds ; and this then implies that Λ is unique.

The cheeks of the coelacanths are unique because the opercular bone is very small and holds a large soft-tissue opercular flap.

This view holds that the U. S. occupies a special niche among developed nations in terms of its national credo, historical evolution, political and religious institutions, and unique origins.

Suppose P is a definable binary relation ( which may be a proper class ) such that for every set x there is a unique set y such that P ( x, y ) holds.

* If the continuum hypothesis holds then is the unique Parovicenko space, up to isomorphism.

This division is illustrated in a number of ways: The sovereign, for example, holds a unique Canadian title and, when she and other members of the Royal Family are acting in public specifically as representatives of Canada, they will use, where possible, Canadian symbols, including the country's national flag, unique royal symbols, armed forces uniforms, and the like, as well as Canadian Forces aircraft or other Canadian-owned vehicles for travel.

" Rather, as legal subjects of the country's monarch, the Royal Family holds a unique position reflected in the confusion that sometimes arises around the awarding of honours to them.

Some have argued that the unique control that curator Jon Hendricks holds over a major historical Fluxus collection ( the Gilbert and Lila Silverman collection ) has enabled him to influence, through the numerous books and catalogues subsidized by the collection, the view that Fluxus died with Maciunas.

Lancaster has several unique ties to the British monarchy ; the House of Lancaster was a branch of the English royal family, whilst the Duchy of Lancaster holds large estates on behalf of Elizabeth II, who herself is also the Duke of Lancaster.

To celebrate this unique breed, the county holds an annual festival known as Goats, Music and More drawing visitors from around the world.

MIA is unique among American airports in that all of its facilities are common-use, meaning that they are assigned by the airport and no one airline holds ownership or leases on any terminal space or gates, thus giving the airport much more flexibility in terminal and gate assignments and allowing it to make full use of existing facilities.

Guyler holds a unique place in theatrical history, having ' acted ' in every performance of The Mousetrap since the opening night on 6 October 1952 in Nottingham.

In addition, the senior warrant officer in the Australian Army holds the unique rank of Warrant Officer ( introduced in 1991 and senior to WO1 ) and the appointment of Regimental Sergeant Major of the Army ( RSM-A ).

The published story was regarded by Robert E. Howard ( the creator of Conan ) as " a masterpiece, which I am sure will live as one of the highest achievements of literature .... Mr. Lovecraft holds a unique position in the literary world ; he has grasped, to all intents, the worlds outside our paltry ken.

Unlike all the other Christian theological systems, preterism holds an exclusive and unique view on the nature and timing of the ' End Times ', in that preterists teach the ' end times ' to be in the 1st century AD.

One can show that every prime element is irreducible ; the converse is not true in general but holds in unique factorization domains.

The Lynx holds the distinction of being the world's first handheld electronic game with a color LCD.

The Economics Department, whose prominent professors include David Blanchflower and Andrew Samwick, also holds the distinction as the top-ranked bachelor's-only economics program in the world.

One key distinction is the purpose for the practice ; handloaders often seek smaller batches of high-quality ammunition, whereas reloaders are said to make large quantities of ammunition that does not need to be of as high quality but at least one authority ( McPherson ) holds that a better distinction for these connotations is that, regardless of quantity, handloads tend to be of generally high quality while reloads tend to be merely functional.

Iraq holds a special distinction in the history of geography: a clay tablet generally accepted as " the earliest known map " was unearthed in 1930 during the excavation of Ga-Sur at Nuzi Yorghan Tepe, near the towns of Harran and Kirkuk, north of the site of Babylon.

Unusually, Yeats holds the distinction of being Ireland's first medalist at the Olympic Games in the wake of creation of the Irish Free State.

Nasal and oral vowels probably merged around the 11th c. in most of Old East Norse .< sup >: 3 </ sup > However, the distinction still holds in Dalarna .< sup >: 4 </ sup > The dots in the following vowel table separate the oral from nasal phonemes.

The materialistic view of the mind-body problem holds that mental disorders arise from physical processes ; in this view, the distinction between brain and mind, and therefore between organic and functional disease, is an artificial one.

the first science-fiction novel in the Shona language, which also holds the distinction of being the first novel in the Shona language to appear as an ebook first before it came out in print.

The film holds the distinction of being the musical film with the most Academy Award wins ( 10 wins ), including Best Picture.

Buick holds the distinction as the oldest active American make.

The 80 by 120 Foot Wind Tunnel at NASA Ames Research Center holds the distinction of being the largest wind tunnel test section in the world.

Miami holds the distinction of being " the only major city in the United States conceived by a woman, Julia Tuttle ", who was a local citrus grower and a wealthy Cleveland native.

Along the Willimantic River ( and border of Mansfield ) stands the Brigham Tavern, which holds the distinction of having housed George Washington around the period of the Revolutionary War.

The country is currently the only nation in Latin America that holds this distinction.

Tao also holds the distinction of being the youngest medalist with his 1986 bronze medal, alongside 2009 bronze medalist Raúl Chávez Sarmiento ( Peru ), at the age of 10 and 11 respectively.

This crossing point holds the distinction of being the highest low point of any U. S. state.

, Jimmy Long's younger brother Gerald Long holds the distinction of being the only current Long in public office and the first Republican among the Long Democratic dynasty.

Five Points holds the distinction of being the first town of its size to receive electricity from Alabama Power in 1925.

Organized by the Warren Chamber of Commerce, the festival celebrates the South Arkansas Vine Ripe Pink Tomato, a special variety of tomato which holds the distinction of being Arkansas ' state fruit and state vegetable.

The Hialeah Park Race Track also holds the dual distinction of being an Audubon Bird Sanctuary due to its famous pink flamingos and being listed on the National Register of Historic Places.

The town holds the distinction of the having the highest percentage of people with Swiss ancestry, followed by nearby Berne, Indiana, according to the 2000 U. S. Census.

At eight state baseball titles, La Porte High School holds the distinction of winning the greatest number in Indiana.

It holds the distinction of being " The Coldest Spot in Iowa ," having recorded a temperature of 47 degrees below zero without wind chill on January 12, 1912.

Concordia holds the distinction of being elected the county seat before the town was created.