hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Diaconescu's theorem
In mathematical logic, Diaconescu's theorem, or the Goodman–Myhill theorem, states that the full axiom of choice is sufficient to derive the law of the excluded middle or restricted forms of it.

The theorem was discovered in 1975 by Radu Diaconescu and later by Nicolas Goodman and John Myhill. Already in 1967, Errett Bishop posed the theorem as an exercise (Problem 2 on page 58 in Foundations of constructive analysis).

Finite set
In mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically mathematical objects, such as numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets.

Informally, a finite set is a set which one could in principle count and finish counting.  For example,

is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the cardinality (or the cardinal number) of the set. A set that is not a finite set is called an infinite set. For example, the set 

of all positive integers is infinite.

Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.
Mary Kelly (playwright)
Mary Elfreda Kelly OBE (25 March 1888 – 5 November 1951) was a British playwright, pageant maker and founder of the Village Drama Society in 1919. Her family home was Kelly House in the village of Kelly, Devon.

Women's Institute
The Women's Institute (WI) is a community-based organization for women in Canada, the United Kingdom, South Africa and New Zealand. The movement was founded in Stoney Creek, Ontario, Canada, by Erland and Janet Lee with Adelaide Hoodless being the first speaker in 1897. It was based on the British concept of Women's Guilds, created by Rev. Archibald Charteris in 1887 and originally confined to the Church of Scotland. From Canada, the organization spread back to Britain, throughout the British Empire and Commonwealth, and to other countries. Many WIs belong to the Associated Country Women of the World organization.
The Wind from Nowhere
The Wind from Nowhere is a science fiction novel by English author J. G. Ballard. Published in 1962, it was his debut novel. He had previously published only short stories.

The novel was the first of a series of Ballard novels dealing with scenarios of natural disaster. Here, civilization is reduced to ruins by prolonged worldwide hurricane-force winds.

As an added dimension, Ballard explores the ways in which disaster and tragedy can bond people together in ways that no normal experiences ever could. That is another recurring theme in his works and makes one of its first appearances here. Some critics have suggested that his first four novels are based on elemental themes, showing global destruction by air, water, fire and earth.

Ballard later dismissed the novel, written in ten days, as a "piece of hackwork", referring instead to The Drowned World as his first real novel.

Tragedy (event)
A tragedy is an event of great loss, usually of human life.  Such an event is said to be tragic. Traditionally, the event would require "some element of moral failure, some flaw in character, or some extraordinary combination of elements" to be tragic.

Not every death is considered a tragedy. Rather, it is a precise set of symptoms surrounding the loss that define it as such. There are a variety of factors that define a death as tragic.

An event in which a massive number of deaths occur may be seen as a tragedy. This can be re-enforced by media attention or other public outcry.

A tragedy does not necessarily involve massive death. The death of a single person, e.g., a public figure or a child, may be seen as a tragedy. The person need not necessarily have been famous before death.
Fazil (film)
Fazil is a 1928 American synchronized sound drama film directed by Howard Hawks and written by Philip Klein and Seton I. Miller. The film stars Charles Farrell, Greta Nissen, John Boles, Mae Busch, Tyler Brooke and John T. Murray. While the film has no audible dialog, it was released with a synchronized musical score with sound effects using the sound-on-film movietone process. The film was released on June 4, 1928, by Fox Film Corporation.

Sound-on-film
Sound-on-film is a class of sound film processes where the sound accompanying a picture is recorded on photographic film, usually, but not always, the same strip of film carrying the picture.  Sound-on-film processes can either record an analog sound track or digital sound track, and may record the signal either optically or magnetically. Earlier technologies were sound-on-disc, meaning the film's soundtrack would be on a separate phonograph record.
Kagarol
Kagarol is a village in the Agra district of Uttar Pradesh state in India. It is situated at a distance of about 25 kilometers to the south-west of Agra city. This village finds mention in some of the earliest Archaeological Survey of India reports compiled by Alexander Cunningham and his assistants, J. D. Beglar and A. C. L. Carlleyle.

Archaeological Survey of India
The Archaeological Survey of India (ASI) is an Indian government agency that is responsible for archaeological research and the conservation and preservation of cultural historical monuments in the country. It was founded in 1861 by Alexander Cunningham during the British Raj who also became its first Director-General.
1870 Southwark by-election
The 1870 Southwark by-election was fought on 17 February 1870.  The by-election was fought due to the resignation (Ambassador to Spain) of the incumbent MP of the Liberal Party, Austen Henry Layard.  It was won by the Conservative candidate Marcus Beresford.

Southwark (UK Parliament constituency)
Southwark (/ˈsʌðərk/ ⓘ SUDH-ərk) was a constituency centred on the Southwark district of South London. It returned two Members of Parliament to the House of Commons of the English Parliament from 1295 to 1707, to the Parliament of Great Britain from 1707 to 1800, and to the UK Parliament until its first abolition for the 1885 general election.  A seat of the same name, covering a smaller area than the last form of the earlier seat in the west of the original and beyond its boundaries to the southwest, was created in 1950 and abolished in 1974.

In its last creation the seat's broad electorate heavily supported the three successive Labour candidates, who won Southwark with a majority of greater than 36% of the votes cast at its eight elections – an extremely safe seat.
Ambohibe
Ambohibe is a rural municipality in Madagascar. It belongs to the district of Vavatenina, which is a part of Analanjirofo Region. The population of the commune was estimated to be approximately 16,000 in 2001 commune census.

Primary and junior level secondary education are available in town. The majority 95% of the population of the commune are farmers.  The most important crop is coffee, while other important products are bananas, cloves and lychee.  Services provide employment for 5% of the population.

Analanjirofo
Analanjirofo is a region in northeastern Madagascar. It is a part of Toamasina Province. It borders the regions of Ambatosoa to the north, Sofia to the west, Alaotra-Mangoro to the southwest and Atsinanana to the south.

The capital of the region is Fenoarivo Atsinanana (French: Fénérive Est). In 2023 the region of Ambatosoa was created from the districts of Mananara Avaratra and Maroantsetra in the northern part of Analanjirofo, although Ambatosoa was not officially inaugurated until 26 July 2025. Since the creation of Ambatosoa, the area of the four districts making up Analanjirofo is 11,188 square kilometres (4,320 sq mi).
Lucio Lombardo-Radice
Lucio Lombardo-Radice (Catania, 10 July 1916; Brussels, 21 November 1982) was an Italian mathematician. A student of Gaetano Scorza, Lombardo-Radice contributed to finite geometry and geometric combinatorics together with Guido Zappa and Beniamino Segre, and wrote important works concerning the Non-Desarguesian plane. He was also a leading member of the Italian Communist Party and a member of its central committee. He had a long professional and political friendship with German natural scientist and dissident Robert Havemann.

Lombardo-Radice's parents were Giuseppe Lombardo Radice and Gemma Harasim. His children included the writer Marco Lombardo Radice and actor Giovanni Lombardo Radice.

The Istituto Tecnico Statale Commerciale "Lucio Lombardo Radice" per Programmatori, a school in Rome, Italy, founded in 1982 as the XXV Istituto Tecnico Commerciale per Programmatori, was in 1992 renamed after Lombardo-Radice. It is now named Istituto di Istruzione Superiore Lombardo Radice

Gaetano Scorza
Bernardino Gaetano Scorza (29 September 1876, in Morano Calabro – 6 August 1939, in Rome) was an Italian mathematician working in algebraic geometry, whose work inspired the theory of Scorza varieties.
Lola.com
Lola.com was a software as a service (SaaS) company based in Boston, Massachusetts. It was best known for developing corporate travel management and expense software for web browsers, the App Store and Google Play. The company was founded in 2015 by former Kayak.com executives, Paul M. English and Bill O'Donnell.

The website operated under a travel agency model for hotel and flight search information as well as booking services for businesses. It also had administrative analytics on employee travel and associated costs. Lola had received more than $80 million in funding since its foundation.

Kayak (company)
Kayak (styled as KAYAK) is a metasearch engine for travel services, including airline flights, hotels, rental cars, and vacation packages. It is owned and operated by Booking Holdings.

Kayak's website and mobile apps are currently available in about 20 languages and 30 countries, including the United States, the United Kingdom, Canada, India, China, France, Germany, Italy, Spain, Russia, Switzerland, Norway, Sweden, Finland, the Netherlands, Australia, Ireland, Mexico, New Zealand, Belgium, Korea, Japan, and Singapore.
Circulene
A circulene is a macrocyclic arene in which a central polygon is surrounded and fused by benzenoids. Nomenclature within this class of molecules is based on the number of benzene rings surrounding the core, which is equivalent to the size of the central polygon. Examples which have been synthesized include  [5]circulene (corannulene), [6]circulene (coronene), [7]circulene, and [12]circulene (kekulene) These compounds belong to a larger class of geodesic polyarenes. Whereas [5]circulene is bowl-shaped and [6]circulene is planar, [7]circulene has a unique saddle-shaped structure (compare to cones and partial cones in calixarenes). The helicenes are a conceptually related class of structures in which the array of benzene rings form an open helix rather than a closed ring.

Helix
A helix (/ˈhiːlɪks/; pl. helices) is a shape like a cylindrical coil spring or the thread of a machine screw. It is a type of smooth skew curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word helix comes from the Greek word ἕλιξ, "twisted, curved". 
A "filled-in" helix – for example, a "spiral" (helical) ramp – is a surface called a helicoid.
2010 FIFA World Cup Group H
Group H of the 2010 FIFA World Cup began on 16 June and ended on 25 June 2010. The group consisted of Switzerland, Honduras, Chile and reigning European (and eventual) champions Spain.

Chile and Spain were in the same group in 1950, in a group from which only the Spanish team qualified for the next round. Chile and Switzerland were also in the same group in 1962, when Chile was host and went on to finish in third place. Switzerland and Spain competed in the same group in 1966, but neither advanced to the next round. Finally, Honduras and Spain were in the same group in 1982. Four years later, in the next World Cup, Chile and Spain would meet again in Group B, against the Netherlands and Australia; Chile would upset Spain 2–0 in their second match, eliminating Spain from the tournament.

1950 FIFA World Cup
The 1950 FIFA World Cup was the fourth edition of the FIFA World Cup, the quadrennial international football championship for senior men's national teams. It was held in Brazil from 24 June to 16 July 1950.

It was the first World Cup tournament in over twelve years, as the 1942 and 1946 World Cups were cancelled due to World War II. Italy, the two-time defending champions, were eliminated in the first round for the first time in history. Uruguay, who had won the inaugural competition in 1930, defeated the host nation, Brazil, in the deciding match of the four-team group of the final round, causing what is sometimes known as one of the biggest upsets in sports history, occasionally called the Maracanaço. This was the only tournament not decided by a one-match final. It was also the inaugural tournament where the trophy was referred to as the Jules Rimet Cup, to mark the 25th anniversary of Jules Rimet's presidency of FIFA.
Tradewest
Tradewest, Inc. was an American video game company based in Corsicana, Texas that produced numerous games in the 1980s and early 1990s. The company was the publisher of the Battletoads and Double Dragon series in North America and the PAL region. In 1994, the company was acquired by WMS Industries and became Midway Home Entertainment when WMS spun off its video game operations as Midway Games.

The name was revived in August 2009 when the head of Midway's European subsidiaries acquired the trademark from Midway in the latter's bankruptcy.

PAL
Phase Alternating Line (PAL) is a colour encoding system for analogue television. It was one of three major analogue colour television standards, the others being NTSC and SECAM. In most countries it was broadcast at 625 lines, 50 fields (25 frames) per second, and associated with CCIR analogue broadcast television systems B, D, G, H, I and K. The articles on analogue broadcast television systems further describe frame rates, image resolution, and audio modulation.

PAL was developed by Walter Bruch at Telefunken in Hanover, West Germany, with important input from Gerhard Mahler. The format was patented by Telefunken in December 1962, citing Bruch as inventor, and unveiled to members of the European Broadcasting Union (EBU) on 3 January 1963. When asked why the system was named "PAL" and not "Bruch", the inventor answered that a "Bruch system" would probably not have sold very well ("Bruch" is the German word for "breakage").
Patrice Manuel
Patrice Manuel (born February 13, 1974) is a retired French alpine skier.

He competed in two events at the 1993 Junior World Championships, recording 13th and 8th places. He made his World Cup debut in January 1995 in Kranjska Gora and competed extensively until 2002.

He collected his first World Cup points with a 26th place in February 1995 in Furano, and improved to 25th place within the end of the year, in December 1995 in Val d'Isere. Manuel later reached 23rd place in November 1997 in Park City, in January 1998 in Adelboden and February 2000 in St. Anton before improving to 19th in the next race in St. Anton. This mark was also equalled twice, in November 2000 in Lake Louise and January 2001 in Kitzbühel. His last World Cup outing came in March 2002 in Kvitfjell.

He represented the club CSH Briancon.

St Anton am Arlberg
Sankt Anton am Arlberg, commonly referred to as St Anton, is a village and ski resort in the Austrian state of Tyrol. It lies in the Tyrolean Alps, with aerial tramways and chairlifts up to 2,811 m (9,222 ft), yielding a vertical drop of 1,507 m (4,944 ft). It is also a popular summer resort among trekkers and mountaineers.

Skiing has a long history in St. Anton: ski instructors from the area emigrated to the United States in the 1930s, helping to popularise the sport. St. Anton was the host of the Alpine World Ski Championships in 2001, and is frequently listed as one of the world's top skiing resorts both in terms of skiing available and après-ski entertainment.
Zhang Chang (Jin dynasty)
Zhang Chang (died 304), also known as Li Chen, was a Man rebel during the Jin dynasty (266–420). In 303, Zhang Chang led a great rebellion against Jin in Jingzhou. Under the guise of restoring the Han dynasty, Zhang Chang propped up a man named Qiu Chen (丘沈), whom he renamed Liu Ni (劉尼), to be a descendant of the Han emperors and the nominal leader of the rebellion. At its peak, Zhang Chang's rebellion encompassed most of the provinces of Jing, Jiang, Xu, Yang and Yu. Despite causing much trouble for Jin, the rebellion only lasted a year before the Inspector of Jingzhou, Liu Hong, defeated and killed him in 304.

Yuzhou (ancient China)
Yuzhou or Yu Province was one of the Nine Provinces of ancient China, later to become an administrative division around the reign of Emperor Wu (r. 141 BC - 87 BC) of the Western Han dynasty (206 BC-AD 9).
Vladimirsky Municipal Okrug
Vladimirsky Municipal Okrug (Russian: Влади́мирский муниципа́льный о́круг) is a municipal okrug in Tsentralny District, one of the eighty-one low-level municipal divisions  of the federal city of St. Petersburg, Russia. As of the 2010 Census, its population was 59,065, up from 57,213 recorded during the 2002 Census.

Administrative divisions of Saint Petersburg
The federal city of Saint Petersburg, Russia, is divided into eighteen rayony ("districts", Russian: районы, singular: rayon), which are in turn subdivided into municipal okrugs, municipal towns, and municipal settlements.
Darren Dietz
Darren Dietz (Kazakh: Даррен Диц; born July 17, 1993) is a Canadian-Kazakhstani professional ice hockey defenceman currently playing for Dinamo Minsk of the Kontinental Hockey League (KHL). He was selected in the fifth round, 138th overall, by the Montreal Canadiens in the 2011 NHL Entry Draft.

HC Dinamo Minsk
Hockey Club Dinamo Minsk or HC Dinamo Minsk (Russian: Дина́мо-Минск; Belarusian: Дынама-Мінск, Dynama-Minsk) is a professional ice hockey club based in Minsk, Belarus. It is a member of the Tarasov Division in the Kontinental Hockey League (KHL).

Dinamo has qualified for the KHL playoffs (Gagarin Cup) nine times: in the 2010–11, 2011–12, 2014–15, 2016–17, 2020–21, 2021–22, 2022–23, 2023–24 and 2024–25 KHL seasons. The team has not won a single round in the Gagarin Cup playoffs, losing in all nine series in a combination of 2nd round and 1st round losses.
Al-Faisaly SC
Al-Faisaly Sports Club (Arabic: نادي الفيصلي الرياضي) is a Jordanian professional football club based in Amman. Founded in 1932, the club competes in the Jordanian Pro League, the top flight of Jordanian football. Nicknamed "the Blue Eagles", they were founded as Al-Ashbal Club in 1932 .

They won 85 official titles, 35 league titles, 21 Jordan FA Cups, 17 Jordan Super Cups, and 10 Jordan FA Shield s being the record holder for all these competitions,  and 2 AFC Cups. Their rivals are Al-Wehdat, a club formed by a Palestinian refugee camp in Amman.

Football in Jordan
The sport of football in the country of Jordan is run by the Jordan Football Association. The association administers the national football team as well as the Jordan League. Association football is the most popular sport in Jordan. Approximately 40% of the people in the country are considered football fans.
Islam in El Salvador
El Salvador is a predominantly Christian country, with adherents Islam being a minuscule minority. Due to the secular nature of the country's constitution, Muslims are free to proselytize and build mosques in the country.

There is a small Muslim community in El Salvador, largely consisting of Yemeni Arabs. However, most of the Palestinian Arab population in the country is Christian. It is estimated that there are about 1,000-1,500 Muslims in El Salvador, however, the figure can reach up to 18,000.

There is an Islamic Cultural Association operated by the Shia community, named Fatimah Az-Zahra. They published the first Islamic magazine in Central America: Revista Biblioteca Islámica. Additionally, they are credited with providing the first and only Islamic library dedicated to spreading Islamic culture in the country. Ahmadiyya Muslim Community also exists in the country.

Dawah
Daʿwah (Arabic: دعوة, Arabic: [ˈdaʕwah], "invitation", also spelt dâvah, daawa, dawah, daawah or dakwah) is the act of proselytizing people to Islam. The plural is daʿwāt (دَعْوات) or daʿawāt (دَعَوات). Preachers who engage in dawah are known as da'i.
The Happy Husband
The Happy Husband is a comedy play by the British-based Australian author Harrison Owen. It premiered at the Theatre Royal, Portsmouth before transferring to the Criterion Theatre in London's West End where it ran for 109 performances between 15 June and 17 September 1927. The London cast included Madge Titheradge, Stella Arbenina, A.E. Matthews, Charles Laughton, Lawrence Grossmith, David Hawthorne, Carl Harbord in his West End debut, Marda Vanne and Ann Trevor. It was produced by Basil Dean. It was staged at the Empire Theatre on Broadway the following year, running for 72 performances.

New Theatre Royal
The Theatre Royal, Portsmouth, is a Victorian Grade II* listed theatre in the heart of Portsmouth, England, with a capacity of 500.  The theatre building was constructed in 1854 as Landport Hall. It was converted to a theatre two years later. It was rebuilt in 1884 by Charles J. Phipps and again in 1900 by Frank Matcham.

The Theatre reopened in October 2015 after a £4.7M refurbishment project.
35th Street Bridge
The 35th Street Bridge crosses the Kanawha River in Charleston, West Virginia, in the United States. It connects Interstate 64/77 south
at Exit #98 with West Virginia Route 61 in northern Kanawha City.

West Virginia Route 61
West Virginia Route 61 is a north–south state highway in central and southern West Virginia. The southern terminus of the route is at West Virginia Route 41 in Piney View. The northern terminus is at U.S. Route 60 (Patrick Street Bridge) in Charleston.
Ida Beav Wells
Ida Beav Wells is a North American beaver that lives in the Southwest Side of Chicago, Illinois near Bubbly Creek. The name was the result of a naming competition held by Urban Rivers. She is particularly known for her "remarkably rotund" appearance. After going viral online, her name was selected through a public contest. Her presence is considered a positive indicator of the improving health of the Chicago River.

Urban Rivers
Urban Rivers is a nonprofit organization that aims at restoring the waterways in Chicago, Illinois. The organization is focused on studying and reviving the city's river ecosystem and water health with floating wetlands. The experimental groups success in launching the creation of arguably the world's "first floating eco-park" (The Wild Mile) in their river remediation efforts drew international attention.
Italian submarine Enrico Tazzoli
Enrico Tazzoli is the name of more than one Italian submarine, named after Enrico Tazzoli, a 19th century Italian Patriot.

Enrico Tazzoli (1935), a Calvi-class submarine launched in 1935 and sunk in 1943.

Enrico Tazzoli (S 511), a Gato-class submarine acquired in 1954 and sold in 1972 for scrapping which previously had served in the United States Navy as USS Barb.

Calvi-class submarine
The Calvi class was a class of three submarines built by Oderno-Terni-Orlando in Genoa for the Royal Italian Navy (Italian: Regia Marina). The submarines were built in 1935, and all three served in the Mediterranean at the start of the Second World War. The boats were transferred to the BETASOM Atlantic submarine base at Bordeaux in August 1940.  In December 1941 the boats were used for a rescue mission of 254 sailors from the sunken German auxiliary cruiser Atlantis.  After Calvi had been sunk, Finzi and Tazzoli were selected for conversion to "transport submarines" in order to exchange rare or irreplaceable trade goods with Japan.  Cargo capacity of 160 tons reduced reserve buoyancy from 20–25% to 3.5–6%; and armament was reduced to defensive machine guns.