hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Collapsing algebra
In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduced by Azriel Lévy in 1963.

The collapsing algebra of λω is a complete Boolean algebra with at least λ elements but generated by a countable number of elements. As the size of countably generated complete Boolean algebras is unbounded, this shows that there is no free complete Boolean algebra on a countable number of elements.

Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution).

Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle.
Oaklands, Pambula
Oaklands is a heritage-listed homestead at Princes Highway, Pambula, Bega Valley Shire, New South Wales, Australia. It was built from 1842 by Messrs Robertson, Hall and Rogers. It was also known as Pamboola Station (c. 1833–1842). It was added to the New South Wales State Heritage Register on 20 February 2004.

Bega Valley Shire
The Bega Valley Shire is a local government area located adjacent to the south-eastern coastline of New South Wales, Australia. The Shire was formed in 1981 with the amalgamation of the Municipality of Bega, Imlay Shire and Mumbulla Shire, with its name deriving from the town of Bega. The shire is also known as the Sapphire Coast for tourism and marketing purposes. During the 2019–20 Australian bushfire season, the area was devastated by fire, with 448 houses being destroyed by fire and approximately 365,000 hectares burned, which is 58% of the Shire's total land mass.

The estimated population as at the 2021 census was 35,942.

The current mayor is Russell Fitzpatrick, an independent who joined the Liberal Party in 2023.
2006 Copa de la Reina de Hockey Patines
The 2006 Copa de la Reina de Hockey Patines was the inaugural edition of the Spanish women's rink hockey national cup. It took place on 25 and 26 March 2006 in Burgos, and it was won by CP Voltregà, which defeated CE Arenys de Munt in the final.

Copa de la Reina de Hockey Patines
The Copa de S.M. la Reina de Hockey Patines is an annual cup competition for Spanish women's rink hockey teams organized by the Spanish Skating Federation. First held in 2006, it is currently contested in spring by the top four team's in the OK Liga's table. CP Voltregà is the cup's most successful club with 6 titles, Biesca Gijón have 3 titles, while CP Vilanova and Cerdanyola CH have won one title each.
Encombe House
Encombe House is a privately owned, Grade II* listed country house built in 1735 on the Encombe Estate near the village of Kingston and about 1-mile (1.6 km) inland of Dorset's Jurassic Coast in southern England. The parkland is Grade II* listed in the National Register of Historic Parks and Gardens.

Shaftesbury Abbey
Shaftesbury Abbey was an abbey that housed nuns in Shaftesbury, Dorset. It was founded in about 888, and dissolved in 1539 during the English Reformation by the order of Thomas Cromwell, minister to King Henry VIII. At the time it was the second-wealthiest nunnery in England, behind only Syon Abbey in west London.
2023–24 Duquesne Dukes men's basketball team
The 2023–24 Duquesne Dukes men's basketball team represented Duquesne University during the 2023–24 NCAA Division I men's basketball season. The team was led by seventh-year head coach Keith Dambrot in his final season as head coach, and played their home games at the UPMC Cooper Fieldhouse in Pittsburgh, Pennsylvania as a member of the Atlantic 10 Conference (A-10). They finished the season 25–12, 10–8 in A-10 play, to finish in sixth place. As the 6 seed, they defeated Saint Louis, Dayton, St. Bonaventure and VCU to be champions of the A-10 tournament. As a result, they received the conference's automatic bid to the NCAA tournament for the sixth time in school history and first since 1977. As the No. 11 seed in the East Region, they upset BYU in the first round before losing in the second round to Illinois 89–63.

2023–24 Dayton Flyers men's basketball team
The 2023–24 Dayton Flyers men's basketball team represented the University of Dayton in the 2023–24 NCAA Division I men's basketball season. They were led by head coach, Anthony Grant, in his seventh season with the Flyers. The Flyers played their home games at UD Arena in Dayton, Ohio as members of the Atlantic 10 Conference (A-10). The Dayton Flyers men's basketball team drew an average home attendance of 13,407 in 15 games in 2023–24, the 20th highest in college basketball.
Javi Martínez
Javier "Javi" Martínez Aginaga (Spanish pronunciation: [xaˈβjeɾ ˈxaβi maɾˈtineθ aɣiˈnaɣa]; born 2 September 1988) is a Spanish professional footballer who plays as a defensive midfielder or centre-back for Qatari Second Division club Al Bidda.

He arrived at Athletic Bilbao in 2006, before his 18th birthday, quickly imposing himself as a starter and going on to make 251 appearances over the course of six La Liga seasons, scoring 26 goals. In 2012, he signed for Bayern Munich for €40 million, going on to win nine consecutive Bundesliga titles as well as the UEFA Champions League in 2013 and 2020.

A Spanish international, Martínez was a member of the squads that won the 2010 FIFA World Cup and UEFA Euro 2012, and also played at the 2014 FIFA World Cup.

Franz Beckenbauer Supercup
The Franz Beckenbauer Supercup or German Super Cup is an annual football match in Germany that features the winners of the Bundesliga championship and the DFB-Pokal. The competition is run by the Deutsche Fußball Liga (English: German Football League).
Wildlife of Mongolia
The wildlife of Mongolia consists of flora, fauna and funga found in the harsh habitats dictated by the diverse climatic conditions found throughout the country. In the north, there are salty marshes and fresh-water sources. The centre has desert steppes. In the south, there are semi deserts as well as the hot Gobi Desert in the south, the fifth-largest desert in the world.

About 90% of the landlocked country is covered by deserts or pastures with extreme climatic conditions. Fauna in the wild includes 139 mammal species, 448 bird species (331 of which are migratory and 119 are resident), 76 fish species, 22 reptile species and 6 amphibian species. Grassland and shrubland covers 55 percent of the country. In the steppe zone, forest covers only 6 percent while 36 percent is covered by desert vegetation, and only 1 percent is used for human habitation and agriculture. The vegetation in the eastern steppe region is grassland (the largest of its type in the world).

Hustai National Park
Hustai National Park (Mongolian: Хустайн байгалийн цогцолборт газар), located in the Khustai Mountains of Töv Province, is a national park of Mongolia. It is also known as Khustain Nuruu National Park. It covers an area of 506 km2 (195 sq mi). The Tuul River runs through the park.
XX Virginis
XX Virginis is a variable star in the equatorial constellation of Virgo, abbreviated XX Vir. It ranges in apparent visual magnitude from 11.55 to 12.78, which is much too faint to be visible to the naked eye. The star is located at an estimated distance of roughly 9,400 light-years (2,900 pc).

This is classified as a type II Cepheid of the BL Her type, having a short pulsation period of 1.348 days. However, a 2014 survey has it classified as an anomalous Cepheid of the BL Boo type. The light curve is asymmetrical, resembling that of a type ab RR Lyrae variable. On the HR diagram it is positioned above the horizontal branch. For this reason, it is sometimes used as the prototype of, "Above Horizontal Branch variables of subtype 1."

This is a very metal-poor star with an estimated 0.6 times the mass of the Sun. The effective temperature and radius vary depending on the phase of the pulsation cycle.

Virgo (constellation)
Virgo is one of the constellations of the zodiac. The name means "maiden" in Latin and its traditional astrological symbol is . Between Leo to the west and Libra to the east, lying in the south, it is the second-largest constellation in the sky (after Hydra) and the largest constellation in the zodiac. The ecliptic intersects the celestial equator within this constellation and Pisces. Underlying these technical two definitions, the sun passes directly overhead of the equator, within this constellation, at the September equinox. Virgo can be easily found through its brightest star, Spica, (in Latin "grain headed").
NGC 5068
NGC 5068 is a face-on field barred spiral galaxy in the Virgo constellation. NGC 5068 is located approximately 22 million light-years away and has a diameter that exceeds 45000 light-years. It was discovered by German-British astronomer William Herschel on 10 March 1785.

Although no supernovae have been observed in NGC 5068 yet, a luminous red nova, designated AT 2020hat (type LRN, mag. 17.8), was discovered by ATLAS on 12 April 2020.

Field galaxy
A field galaxy is a galaxy that does not belong to a larger galaxy group or cluster and hence is gravitationally alone.

Roughly 80% of all galaxies located within 5 Mpc (16 Mly) of the Milky Way are in groups or clusters of galaxies. Most low-surface-brightness galaxies are field galaxies. The median Hubble-type of field galaxies is Sb, a type of spiral galaxy.
Rinchen Barsbold
Rinchen Barsbold (Mongolian: Ринченгийн Барсболд, Rinchyengiin Barsbold; 21 December 1935 – 28 August 2025) was a Mongolian paleontologist, geologist and an expert in vertebrate paleontology and Mesozoic stratigraphy. Most of his work was performed at the Institute of Geology in Ulaanbaatar. Barsbold was instrumental in the discovery and recovery of the Mongolian dinosaur fossil record. His work has helped to form a more complete understanding of the later stages of dinosaur evolution in Eurasia.

Oviraptoridae
Oviraptoridae is a group of bird-like, herbivorous or omnivorous maniraptoran dinosaurs. Oviraptorids are characterized by their toothless, parrot-like beaks and, in some cases, elaborate crests. They were generally small, measuring between one and two metres long in most cases, though some possible oviraptorids were enormous. Oviraptorids are currently known only from the Late Cretaceous in Asia, with the most well-known species and complete specimens found only in the Gobi Desert of Mongolia and northwestern China.
Nakuru County
Nakuru County is located in Kenya. It is number 32 out of the 47 Kenyan counties. Nakuru is a host to Kenya's Fourth City – Nakuru City, whereby it was awarded a City Charter on 1 December 2021, by President Uhuru Kenyatta, ranking it with Nairobi, Mombasa, and Kisumu, as the other big cities in Kenya. With a population of 453,000 as per 2025 census, it is the third most populous county in Kenya after Nairobi County and Kiambu County, in that order. With an area of 7,496.5 km2,  it is Kenya's 19th largest county in size. Until 21 August 2010, it formed part of Rift Valley Province.

Nairobi City County
Nairobi City County is one of the 47 Counties of Kenya and serves as the capital of Kenya. It is the most populous county as of the 2019 census with a population of 4,397,073, yet among the smallest in area at 696.1 km². Despite its small size, Nairobi County contributes approximately 27.5% of Kenya's Gross Domestic Product, making it the economic powerhouse of the nation.

The county was established on 4 March 2013 under Kenya's new constitution, replacing the former Nairobi Province administrative unit. It comprises 17 constituencies and 85 electoral wards, with 11 gazetted sub-counties for administrative purposes.
1996 Skoda Czech Open
The 1996 Skoda Czech Open was a men's tennis tournament played on outdoor clay courts at the I. Czech Lawn Tennis Club in Prague, Czech Republic and was part of the World Series of the 1996 ATP Tour. It was the tenth edition of the tournament and ran from 29 April until 5 May 1996. Second-seeded Yevgeny Kafelnikov won the singles title.

1996 ATP Tour
The Association of Tennis Professionals (ATP) Tour is the elite tour for professional tennis organized by the ATP. The ATP Tour includes the Grand Slam tournaments (organized by the International Tennis Federation (ITF)), the ATP Super 9, the ATP Championship Series, the ATP World Series, the ATP World Team Cup, the Davis Cup (organized by the ITF), the ATP Tour World Championships and the Grand Slam Cup (organized by the ITF).
Inghams
Ingham's is a supplier/producer of poultry and fodder across Australia and New Zealand. The company claims to be one of the largest producers of chicken and turkey products in Australia and employs in excess of 8,000 people in more than 100 locations in Australia and New Zealand. The company was founded in 1918 and was managed by members of the Ingham family from its establishment until 2014, including Walter Ingham and his two sons, Jack Ingham and Bob Ingham. TPG Capital acquired Ingham's in 2014 for A$880 million. Ingham's was listed on the Australian Securities Exchange in November 2016.

Australian Securities Exchange
Australian Securities Exchange Ltd (ASX) is an Australian public company that operates Australia's primary securities exchange, the Australian Securities Exchange (sometimes referred to outside of Australia, or confused within Australia, as the Sydney Stock Exchange, which is a separate entity). The ASX was formed on 1 April 1987, through incorporation under legislation by the Parliament of Australia as an amalgamation of the six state securities exchanges. It merged with the Sydney Futures Exchange in 2006.

Today, ASX has an average daily turnover of A$4.685 billion and a market capitalisation of around A$1.6 trillion, making it one of the world's top 20 listed exchange groups and the largest in the southern hemisphere.

ASX Clear is the clearing house for all shares, structured products, warrants and ASX Equity Derivatives.
Armenians in Israel and Palestine
Armenians in Israel and Palestine (Hebrew: ארמנים; Arabic: أَرْمَنِيُّون) make up a community of approximately 5,000–6,000 Armenians living in both Israel and Palestine.

In 1986, it was estimated that 1,500 Armenians lived in the city of Jerusalem. According to a 2006 survey, 790 Armenians lived in Jerusalem's Old City. In 2021, an estimate of approximately 5,000–6,000 Armenians lived across Israel and Palestine.

Armenian Catholic Church
The Armenian Catholic Church is an Eastern Catholic particular church sui iuris of the Catholic Church. It accepts the leadership of the bishop of Rome, and is therefore in full communion with the universal Catholic Church, including the Latin Church and the 22 other Eastern Catholic Churches. The Armenian Catholic Church is regulated by Eastern canon law, summed up in the Code of Canons of the Eastern Churches.

The head of the sui iuris Armenian Catholic Church is the Armenian Catholic patriarch of Cilicia, whose main cathedral and de facto archiepiscopal see is the Cathedral of Saint Elias and Saint Gregory the Illuminator, in Beirut, Lebanon.

Armenian Caritas is the official aid organization of the Catholic Church in Armenia.
Abdication of Juan Carlos I
King Juan Carlos I of Spain announced his pending abdication from the throne on 2 June 2014. An organic law permitting the abdication, required by the 1978 Constitution in its article 57.5, was drafted by the government and approved by the Cortes Generales, and was formally signed on 18 June during a ceremony in the Hall of Columns of the Royal Palace of Madrid. The abdication became effective when it was published in the Official State Gazette at midnight on 19 June.

The Prince of Asturias, Felipe de Borbón y Grecia, succeeded the throne under the name Felipe VI on the abdication of his father. Juan Carlos retained the title of king emeritus with ceremonial functions entrusted to him by Felipe.

Succession to the Spanish throne
Succession to the Spanish throne follows male-preference cognatic primogeniture. A dynast who marries against the express prohibition of the monarch and the Cortes Generales, the legislative chamber of Spain, is excluded from the succession.  Upon proclamation by the Cortes Generales, the monarch is to take an oath to discharge his duties faithfully, to abide by the Constitution and the law and ensure they are abided by, and to respect the rights of the citizens and of the Autonomous Communities.
Tring Rugby
Tring Rugby Club is an English rugby union team based in Tring, Hertfordshire. The club runs four senior teams, two academy teams and a full range of  junior teams. The first XV currently play in Regional 1 South East.

Tring
Tring /trɪŋ/ is a market town and civil parish in the Borough of Dacorum, in Hertfordshire, England. It is situated in a gap passing through the Chiltern Hills, classed as an Area of Outstanding Natural Beauty, 30 miles (50 km) from Central London. Tring is linked to London by the Roman road of Akeman Street, the modern A41 road, the Grand Union Canal and the West Coast Main Line to London Euston. Settlements in Tring date back to prehistoric times and it was mentioned in the Domesday Book; the town received its market charter in 1315. Tring is now largely a commuter town within the London commuter belt.
As of 2021, Tring had a population of 12,427.
Clyst St George
Clyst St George (anciently Clyst Champernowne) is a village and civil parish in East Devon, England, adjoining the River Clyst some 4 miles (6.4 km) southeast of Exeter and 5 miles (8.0 km) north of Exmouth.

East Devon
50°40′44″N 3°14′20″W﻿ / ﻿50.679°N 3.239°W﻿ / 50.679; -3.239

East Devon is a local government district in Devon, England. Its council is based in the town of Honiton, although Exmouth is the largest town. The district also contains the towns of Axminster, Budleigh Salterton, Cranbrook, Ottery St Mary, Seaton and Sidmouth, along with numerous villages and surrounding rural areas.

The district borders Teignbridge and the City of Exeter to the west, Mid Devon to the north, Somerset to the north-east, and Dorset to the east.

Two parts of the district are designated as Areas of Outstanding Natural Beauty: the Blackdown Hills in the north of the district and the East Devon AONB along the district's coast and adjoining areas. The East Devon coastline from Exmouth to the border with Dorset is also part of the designated World Heritage Site of the Jurassic Coast; the designated area continues into Dorset as far as the Old Harry Rocks near Swanage.
2025–26 Formula E World Championship
The 2025–26 ABB FIA Formula E World Championship is the twelfth season of the FIA Formula E championship, a motor racing championship for electrically powered vehicles recognised by motorsport's governing body, the Fédération Internationale de l'Automobile (FIA), as the highest class of competition for electric open-wheel racing cars. It began in December 2025 and will end in August 2026.

It is the fourth and final season of the Formula E Gen3 Evo, with the Gen4 regulations coming into effect the following season.

Porsche Formula E Team
The Porsche Formula E Team, formally the TAGHeuer Porsche Formula E Team, is a German racing team that competes in Formula E, which is organized by the Fédération Internationale de l'Automobile (FIA). The team made its debut in the category at the 2019 Ad Diriyah ePrix, which started the 2019–20 season. They had their first race win at the 2022 Mexico City ePrix. Porsche's factory outfit took their first Formula E driver's championship at the 2024 London ePrix, with driver Pascal Wehrlein. They won the Team's Championship and the Manufacturer's Championship in the 2025 season at the 2025 London ePrix.
Bathmocercus
Bathmocercus is a genus of bird in the family Cisticolidae. 
It contains the following species:

Black-headed rufous warbler (Bathmocercus cerviniventris)

Black-faced rufous warbler (Bathmocercus rufus)

Species from the genus Scepomycter are sometimes placed in this genus though several marked morphological differences are used to justify its separation.

Black-headed rufous warbler
The black-headed rufous warbler (Bathmocercus cerviniventris), also known as the black-capped rufous warbler, is a species of bird in the family Cisticolidae.  It is found in Ivory Coast, Ghana, Guinea, Liberia, and Sierra Leone.  Its natural habitats are subtropical or tropical moist lowland forest, subtropical or tropical swampland, and subtropical or tropical moist montane forest.  It is threatened by habitat loss.

In 2020, the population of this bird in Liberia was estimated to be 60,000 pairs. The bird is rare in Ghana where there have been only one or two records.
Greenbrier (Great Smoky Mountains)
Greenbrier is a valley in the northern Great Smoky Mountains of Tennessee, located in the southeastern United States. Now a recreational area located within the Great Smoky Mountains National Park, Greenbrier was once home to several Appalachian communities.

Greenbrier is situated along the Middle Fork of the Little Pigeon River, stretching from Porters Flat in the south to Emert's Cove in the north, at the present park boundary. The area also includes the Middle Fork's immediate watershed from the crest of Grapeyard Ridge to the west (opposite the Roaring Fork area) to Snag Mountain in the east. The area is sometimes called Big Greenbrier to distinguish it from Little Greenbrier, which is located between Wears Valley and Elkmont several miles to the west.

Wears Valley, Tennessee
Wears Valley (sometimes spelled Wear Valley) is an unincorporated community in Sevier County, Tennessee that was formerly treated by the U.S. Census Bureau as a census county division. As of the 2000 Census, the population of Wears Valley was 6,486.

Wears Valley is situated in a valley known as Wear Cove, which runs parallel to the Great Smoky Mountains National Park.  Like other park border communities, the history and economy of the valley are intertwined with that of the Smokies.

Both are named after Samuel Wear (1753–1817), a Revolutionary War veteran who erected a fort near the entrance to Wear Cove in what is now Pigeon Forge.