OpenLLM-France/wikimedia huggingface dataset:
# Positive set theory

In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension holds for at least the positive formulas $\phi$ (the smallest class of formulas containing atomic membership and equality formulas and closed under conjunction, disjunction, existential and universal quantification).
Typically, the motivation for these theories is topological: the sets are the classes which are closed under a certain topology. The closure conditions for the various constructions allowed in building positive formulas are readily motivated (and one can further justify the use of universal quantifiers bounded in sets to get generalized positive comprehension): the justification of the existential quantifier seems to require that the topology be compact.

## Axioms

The set theory $\mathrm {GPK} _{\infty }^{+}$ of Olivier Esser consists of the following axioms:

### Extensionality

$\forall x\forall y(\forall z(z\in x\leftrightarrow z\in y)\to x=y)$

### Positive comprehension

$\exists x\forall y(y\in x\leftrightarrow \phi (y))$
where $\phi$ is a positive formula. A positive formula uses only the logical constants $\{\top ,\bot ,\land ,\lor ,\forall ,\exists ,=,\in \}$ but not $\{\to ,\neg \}$.

### Closure

$\exists x\forall y(y\in x\leftrightarrow \forall z(\forall w(\phi (w)\rightarrow w\in z)\rightarrow y\in z))$
where $\phi$ is a formula. That is, for every formula $\phi$, the intersection of all sets which contain every $x$ such that $\phi (x)$ exists. This is called the closure of $\{x\mid \phi (x)\}$ and is written in any of the various ways that topological closures can be presented. This can be put more briefly if class language is allowed (any condition on sets defining a class as in NBG): for any class C there is a set which is the intersection of all sets which contain C as a subclass. This is a reasonable principle if the sets are understood as closed classes in a topology.

### Infinity

The von Neumann ordinal $\omega$ exists. This is not an axiom of infinity in the usual sense; if Infinity does not hold, the closure of $\omega$ exists and has itself as its sole additional member (it is certainly infinite); the point of this axiom is that $\omega$ contains no additional elements at all, which boosts the theory from the strength of second order arithmetic to the strength of Morse–Kelley set theory with the proper class ordinal a weakly compact cardinal.

## Interesting properties

* The universal set is a proper set in this theory.
* The sets of this theory are the collections of sets which are closed under a certain topology on the classes.
* The theory can interpret ZFC (by restricting oneself to the class of well-founded sets, which is not itself a set). It in fact interprets a stronger theory (Morse–Kelley set theory with the proper class ordinal a weakly compact cardinal).
# Millennium 3D chess

Millennium 3D chess is a three-dimensional chess variant created by William L. d'Agostino in 2001. It employs three vertically stacked 8×8 boards, with each player controlling a standard set of chess pieces. The inventor describes his objective as "extending the traditional chess game into a multilevel environment without distorting the basic game."

## Rules

Millennium 3D сhess extends the traditional (two-dimensional) game of chess into a multilevel environment.
For notation purposes, the three board levels are denoted 1, 2 (the middle board), and 3. Moves are recorded in the same manner as chess, using algebraic notation, with the only difference that each square is prefaced by its level number. The white and black armies begin, in standard formation, on boards 1 and 3 respectively.
All pieces can always move as normal while staying on the same board. Additionally, every piece is able to move between boards. Each piece's additional permitted movement in the third dimension is extended from its conventional 2D movement as follows:
* The king can move one square up or down, either directly or combined with its regular movement.
* The knight can move up or down one board and two squares orthogonally, or up or down two boards and one square orthogonally. As in standard chess, the knight is the only piece able to move past intervening pieces.
* The bishop can move up or down one or two boards, as long as it also moves the same number of squares in a diagonal direction.
* The rook can move vertically up and down while not moving in the other two dimensions. Additionally, a rook can move an equal number of squares vertically as it does in one of the lateral dimensions.
* The queen moves as the bishop and rook combined.
* The pawn can move one square up or down while staying in the same position laterally, or it can advance one square and additionally move one board up or down. Optionally, the pawn's first move can be two squares vertically, or two squares forward and two squares vertically. The pawn can capture diagonally forwards onto a board immediately above or below it. After a pawn's two-step first move, unless that move was two squares vertically only, the pawn may be captured en passant on the square it passed through. Promotion occurs at the opponent's back rank and starting board; i.e. White promotes at rank 8 of board 3, and Black promotes at rank 1 of board 1.
| 1 | 1 | 1 | 1 | 2 | 3 |
Initial setup :
| 1 | 1 | 1 | 1 | 2 | 3 |
Movement of the rook and knight :
| 1 | 1 | 1 | 1 | 2 | 3 |
Movement of the bishop and queen :
| 1 | 1 | 1 | 1 | 2 | 3 |
Movement of the pawn and king. Squares marked × are capturing moves for the pawns. :

## Example game

George Davis vs. William d'Agostino, corr. 2006:
1. ♘2g3 ♝2b7 2. ♗3e3 ♞3c6 3. ♘2b3 ♝2g7 4. ♘2a5 ♛1b6 5. ♘3c5 ♛×1b2 6. ♘×3b7 ♛3b4 7. ♘3c5 ♛3e1+ 8. ♕2e1 ♛3c3+ 9. ♔2f1 ♛×1a1 10. ♕2c1 ♝2a6+ 11. 2e2 ♛×1a2 12. ♘2c7 ♜2h7 13. ♘1e7+ ♚2e8 14. ♘1c6 ♜1c8 15. ♘×3c7 ♜×1c2 16. ♕2c7 ♛2b1+ 17. ♔1g1 ♞3e5 18. ♕1d7+ ♚2f8 19. ♗2f4 ♛2d1 20. ♗×3e5 ♛3e1+ 21. ♔2g1 ♛×3e5 22. ♕2e7+ ♚1g7 23. ♕×3d7 ♝2d4+ 24. 2e3 ♜2c1+ 25. ♔1g1 ♛3g3+ 26. 2g2 ♜2f1+ 27. ♘×2f1 ♝3e3+ 28. 2f2 ♛×2f2# 0–1
# Kampale

Kampale is a village in the Bassar Prefecture in the Kara Region of north-western Togo.
# Mike Mekelburg

Mike Mekelburg (born February 20, 1975) is a retired American soccer midfielder who played professionally in the USISL and National Professional Soccer League.

## Youth

Mekelburg grew up in Tampa, Florida, playing for Tampa's Black Watch S.C. In 1993, he graduated from George D. Chamberlain High School where he played on the boys' soccer team. In 1992, the Chamberlain soccer team finished runner-up to Killian in the Florida 4A high school soccer championship. Mekelburg attended the University of South Florida, playing for the men's soccer team from 1993 to 1996. He was a 1996 First Team All American.

## Professional

In December 1996, the Tampa Bay Terror selected Mekelburg in the National Professional Soccer League draft. In February 1997, the Tampa Bay Mutiny picked him in the first round (eighth overall) of the 1997 MLS College Draft. Mekelburg signed with the Mutiny, but injuries kept him off the field. The team waived him on June 24, 1997. In July, Dallas Sidekicks then chose Mekelburg in the Continental Indoor Soccer League Supplemental Draft after Mekelburg had trained with them for several weeks. The Sidekicks did not sign him and Mekelburg joined the Baltimore Spirit of the National Professional Soccer League in September 1997. In 1998, he played for the Milwaukee Rampage in the USISL A-League. On January 28, 1999, he signed a two-year contract with the Charleston Battery. On July 24, 1999, the Battery traded Mekelburg to the Raleigh Capital Express in exchange for Edmundo Rodriguez.
# Ancylolomia laverna

Ancylolomia laverna is a moth in the genus Ancylolomia in the family Crambidae. It was described by Stanisław Błeszyński in 1970. It is found in Myanmar.
# Inhaúma, Rio de Janeiro

Inhaúma is a neighborhood in the North Zone of Rio de Janeiro, Brazil.
* This Rio de Janeiro state, Brazil location article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Joseph Partsch

Joseph Partsch (4 July 1851 – 22 June 1925) was a German geographer, born at Schreiberhau, Silesia.

## Biography

He studied at the University of Breslau, receiving his doctorate in 1874, and began teaching at the university (privat-docent, 1875), becoming later a professor of geography. Here he remained until 1905, when on the death of Friedrich Ratzel, he was called to the chair of geography at the University of Leipzig. Here, he served as a full professor of geography up until 1922. He died in Bad Brambach, Vogtland on June 22, 1925.

## Contributions

His earlier writings were devoted to classical geography, but in later years he wrote extensively on glacial geology, the history of geography, and regional geography. In the last group are some of his best-known works, such as the systemic monographs on the Ionian Islands, the standard geography of central Europe, and the geography of Silesia. Among English-speaking people he is best known as the author of "Central Europe" (English, 1903; German, 1904), the English edition, prepared by H. J. Mackinder, appearing in the series "The Regions of the World." This book was of particular value for its account of the physiography of the region which became the battle ground of Europe (1914, et seq.) and especially of the last chapter, "The Conditions of National Defense".

## Partial bibliography

* Physikalische Geographie von Griechenland, mit besonderer Rücksicht auf das Alterthum, Breslau 1885 – Physical Geography of Greece: With special regard to its antiquity.
* Philipp Clüver, der Begründer der historischen Länderkunde. Ein Beitrag zur Geschichte der geographischen Wissenschaft, Wien 1891 – Philipp Clüver, the founder of historical geography.
* Schlesien. Eine Landeskunde für das deutsche Volk auf wissenschaftlicher Grundlage, Breslau 1896 – Silesia: a geography for the German people.
* Mitteleuropa. Die Länder und Völker von den Westalpen und dem Balkan bis an den Kanal und das Kurische Haff, Gotha 1904 – Central Europe: the countries and peoples of the Western Alps and the Balkans, etc.
* Die Hohe Tatra zur Eiszeit, Leipzig 1923 – The High Tatras of the Ice Age.
# Siane Rural LLG

Siane Rural LLG is a local-level government (LLG) of Chimbu Province, Papua New Guinea. The Siane language is spoken in the LLG.

## Wards

* Kereku
* Waisime
* Murefagu
* Marefagu
* Nime-Kaupa
* Mi-Fokowe
* Kumogu
* Atinogu
* Irafaiufa
* Komuni No. 1
* Famundi
* Seine
* Rabiufa
* Rumbuiufa
* Andomono
* Feremena
* Wafo
* Lofaifo
* Loanoi
* Nomanena
* Kemami
* Nomane
* Norifo
* Komborufa
* Foinawa
* Komni No. 2
* Kifiufa
# Calliostoma tsuchiyai

Calliostoma tsuchiyai is a species of sea snail, a marine gastropod mollusk in the family Calliostomatidae.

## Taxonomy

Some authors place this taxon in the subgenus Calliostoma (Tristichotrochus).

## Distribution

This marine species occurs off Japan.
# Helldorado

Helldorado may refer to:
* Helldorado, a nickname for Tombstone, Arizona (a variation of El Dorado) created by a disgruntled miner who wrote a letter in July 1881 to the Tombstone Nugget newspaper complaining about trying to find his fortune and ending up washing dishes
* Helldorado (album), the eighth album by W.A.S.P., released in 1999
* Helldorado (band), a Norwegian Americana band
* Helldorado Days (Las Vegas), a rodeo, parade and festival in Las Vegas, Nevada (first held 1935)
* Helldorado Days (Tombstone), an annual celebration and parade in Tombstone, Arizona (first held 1929)
* Helldorado (video game), a 2007 strategy video game
* Helldorado (film), a 1934 American film, starring Ralph Bellamy
* Heldorado, a 1946 Roy Rogers film set in the Las Vegas Helldorado Days celebrations
# Canton of Bénévent-l'Abbaye

The Canton of Bénévent-l'Abbaye was a canton situated in the Creuse département and in the Limousin region of central France. It was disbanded following the French canton reorganisation which came into effect in March 2015. It consisted of 10 communes, which joined the canton of Le Grand-Bourg in 2015. It had 3,324 inhabitants (2012).

## Geography

An area of farming and forestry in the arrondissement of Guéret, centred on the town of Bénévent-l'Abbaye. The altitude varies from 294 m (Châtelus-le-Marcheix) to 693 m (Saint-Goussaud) with an average altitude of 459 m.
The canton comprised 10 communes:
* Arrènes
* Augères
* Aulon
* Azat-Châtenet
* Bénévent-l'Abbaye
* Ceyroux
* Châtelus-le-Marcheix
* Marsac
* Mourioux-Vieilleville
* Saint-Goussaud

## Population

Historical population of Canton of Bénévent-l'Abbaye (Source: INSEE) :
| Year | 1962 | 1968 | 1975 | 1982 | 1990 | 1999 |
| Population | 4805 | 5305 | 4750 | 4248 | 3734 | 3495 |
| From the year 1962 on: No double counting—residents of multiple communes (e.g. students and military personnel) are counted only once. |||||||
# Abaeté Futebol Clube

Abaeté Futebol Clube, commonly known as Abaeté, is a Brazilian football club based in Abaetetuba, Pará state. They competed in the Série C once.

## History

The club was founded on March 5, 1936. They won the Campeonato Paraense Second Level in 2004. Abaeté competed in the Série C in 2005, when they were eliminated in the Third Stage by fellow Pará state club Remo.

## Achievements

* Campeonato Paraense Second Level:
** Winners (1): 2004

## Stadium

Abaeté Futebol Clube play their home games at Estádio Humberto Parente. The stadium has a maximum capacity of 3,100 people.
# Iris orientalis (insect)

Iris orientalis is a species of praying mantis found in Asia.

## Range

Afghanistan, Java, India, Nepal, Pakistan (NW-Himalaya: Kulu Valley, Kangra ).
# Irish manual alphabet

The Irish manual alphabet is the manual alphabet used in Irish Sign Language. Compared with other manual alphabets based on the Latin alphabet, it has unusual forms for the letters G, K, L, P, and Q.
* Irish manual alphabet
* A
* B
* C
* D
* E
* F
* G
* H
* I
* J
* K
* L
* M
* N
* O
* P
* Q
* R
* S
* T
* U
* V
* W
* X
* Y
* Z
# André Sardet

André Miraldo Sardet Pires is a Portuguese singer and musician, born in the city of Coimbra on 8 January 1976. Acústico (2006), his most successful work, sold over 120,000 copies and was recorded live at Associação Académica de Coimbra's Teatro Académico de Gil Vicente, in Coimbra. "Foi feitiço" is among his best known hits.

## Personal life

André Sardet started his singing career at 19 years old. He attended a mechanical technical engineering course at the Instituto Superior de Engenharia de Coimbra (ISEC), but dropped out in order to pursue his career in music. Sardet is married with children, living with his family in Coimbra. His surname, Sardet, is uncommon in Portuguese and comes from a great-grandfather, a French conductor who migrated to Portugal.

## Discography
### Albums

* Imagens (1996)
* Agitar Antes de Usar (1998)
* André Sardet (album) (2002)
* Acústico (2006 live album)
* Mundo de Cartão (2008)
* Mundo de Cartão ao vivo (2009 live album)
* Pára, escuta e olha (2011)
# Sympis

Sympis is a genus of moths of the family Noctuidae erected by Achille Guenée in 1852.

## Description

Palpi upturned and smoothly scaled, where the second joint reaching above vertex of head and long slightly curved third joint. Antennae ciliated in male. Thorax and abdomen smoothly scaled. Tibia spineless, and hairy. The first joint of hind tarsi hairy on the upperside. Forewings with somewhat produced and acute apex.

## Species

* Sympis ochreobasis Pagenstecher, 1900
* Sympis parkeri Lucas, 1894
* Sympis rufibasis Guenée, 1852
# Schedule X

Schedule X is a class of prescription drugs in India appearing as an appendix to the Drugs and Cosmetics Rules introduced in 1945. These are drugs which cannot be purchased over the counter without a valid prescription of a Registered Medical Practitioner (RMP). Also, the retailer has to preserve the prescription for a period of two years.

## Included drugs

The following are the Schedule X drugs mentioned in the Drugs and Cosmetics Rules 1945:
The list of Schedule X drugs:
* Amobarbital
* Amphetamine
* Barbital
* Cyclobarbital
* Dexamphetamine
* Ethchlorvynol
* Glutethimide
* Ketamine
* Meprobamate
* Methamphetamine
* Methylphenidate
* Methylphenobarbital
* Pentobarbital
* Phencyclidine
* Phenmetrazine
* Secobarbital
Preparations containing the above substances are also covered by this Schedule. Any stereoisometric form of the substance specified in this Schedule, any salt of the substance and preparation containing such substances are also covered by this Schedule.
# Synaphea endothrix

Synaphea endothrix is a shrub endemic to Western Australia.
The erect and clumped shrub typically grows to a height of 0.6 metres (2 ft) and usually blooms between August and September producing yellow flowers.
It is found on lateritic rises along the west coast in the Wheatbelt region of Western Australia between Coorow and Dandaragan where it grows in sandy-loamy-gravelly soils over laterite.
# Syria at the 2019 World Athletics Championships

Syria competed at the 2019 World Athletics Championships in Doha, Qatar, from 27 September–6 October 2019.

## Result
### Key

* Note–Ranks given for track events are for the entire round
* Q = Qualified for the next round
* q = Qualified for the next round as a fastest loser or, in field events, by position without achieving the qualifying target
* NR = National record
* GR = Games record
* PB = Personal best
* SB = Season best
* DNF = Did not finish
* DNS = Did not start
* NM = No mark
* N/A = Round not applicable for the event
* Bye = Athlete not required to compete in round

### Men
#### Field events

| Athlete | Event | Qualification | Qualification | Final | Final |
| Athlete | Event | Distance | Position | Distance | Position |
| Majd Eddin Ghazal | High jump | 2.17 | 14 | Did not advance | Did not advance |
# Syria at the 2018 Mediterranean Games

Syria competed at the 2018 Mediterranean Games in Tarragona, Spain from 22 June to 1 July 2018.

## Medals

| Medal | Name | Sport | Event | Date |
| Gold | Majd Eddin Ghazal | Athletics | Men's High Jump | 29 June |
| Gold | Ahmed Ghousoon | Boxing | Men's middleweight | 30 June |
| Silver | Ali Al Hazzaa | Weightlifting | Men's 94 kg Clean & Jerk | 27 June |
| Silver | Hussein Al Masri | Boxing | Men's flyweight | 30 June |
| Bronze | Abdul Karim al-Hassan | Wrestling | Men's 67 kg | 26 June |
| Bronze | Majd Hassan | Weightlifting | Men's 105 kg Clean & Jerk | 26 June |
| Bronze | Mohamad Mulayes | Boxing | Men's super heavyweight | 30 June |
Medals by sport :
| Sport | | | | Total |
| Athletics | 1 | 0 | 0 | 1 |
| Box | 1 | 1 | 1 | 3 |
| Weightlifting | 0 | 1 | 1 | 2 |
| Wrestling | 0 | 0 | 1 | 1 |
| Total | 2 | 2 | 3 | 7 |

## Weightlifting

Ali Alhazzaa won the silver medal in the men's 94 kg Clean & Jerk event. Majd Hassan won the bronze medal in the men's 105 kg Clean & Jerk event.
# Mission Stadium

Mission Stadium was a multi-purpose stadium in San Antonio, Texas, United States. It was opened in 1947 as the stadium of the San Antonio Missions of the Texas League. Its final season was in 1964; V. J. Keefe Memorial Stadium replaced it in 1968 when minor league baseball returned to San Antonio. The capacity of the stadium was 10,000 spectators.
The ballpark was bounded by Mission Road (west and north, third base and left field); Mitchell Street (south, first base); and Steves Avenue (north and east, center field and right field). The site is currently a parking lot for an office complex, whose curvature near the streetcorner approximates the curvature of the old grandstand.

## Sources

* "https://www.milb.com/san-antonio/ballpark/wolff-stadium
# Charles Elliott

Charles Elliott may refer to:
* Charles Elliott (New Zealand politician) (1811–1876), New Zealand politician
* Charles Elliott (Australian politician) (1870–1938), member of the Western Australian Legislative Council
* Sir Charles Alfred Elliott (1835–1911), Lieutenant Governor of Bengal
* Charles B. Elliott (1861–1935), American jurist
* Charles Loring Elliott (1812–1868), American portrait painter
* Charles Elliott (footballer) (1896–1940), English footballer
* Charles W. Elliott, British Columbia First Nations woodcarver
* C. Thomas Elliott (born 1939), physicist
* Charles Boileau Elliott (1803–1875), English cleric and travel writer
* Charles Irving Elliott (1892–1972), pioneer aviator in the Hawaiian Islands
# Miss Rwanda 2015

Miss Rwanda 2015, the fifth edition of the Miss Rwanda pageant, was held on 22 February 2015 at Kigali Serena Hotel in the province of Kigali.
The winner, Doriane Kundwa succeeded Colombe Akiwacu, Miss Rwanda 2014.
Joannah Keza Bagwire, has finished 4th runner-up at Miss Heritage Global 2015.

## Results

| Final Results | Contestant |
| Miss Rwanda 2015 | Northern Province - Doriane Kundwa |
| 1st Runner-up | Kigali - Vanessa Raissa Uwase |
| 2nd Runner-up | Eastern Province - Lynca Akacu |
| 3rd Runner-up | Eastern Province - Fiona Mutoni Naringwa |
| 4th Runner-up | Eastern Province - Balbine Mutoni |

### Special Awards

* Miss Congeniality - Joannah Keza Bagwire (Southern Province)
* Miss Photogenic - Sabrina Kalisi Ihozo (Western Province)
* Miss Popularity - Doriane Kundwa (Northern Province)
* Miss Heritage - Darlene Gasana (Western Province)

## Contestants

| Province represented | Name | Age | Height (cm) |
| Northern Province | Colombe Uwase | 19 | 170 |
| Northern Province | Doriane Kundwa | 19 | 174 |
| Western Province | Darlene Edna Gasana | 19 | 173 |
| Western Province | Colombe Uwase | 19 | 170 |
| Western Province | Flora Mutoniwase | 21 | 173 |
| Western Province | Vanessa Mpogazi | 19 | 179 |
| Western Province | Sabrina Ihozo | 21 | 175 |
| Southern Province | Joannah Keza Bagwire | 18 | 175 |
| Southern Province | Joelle Ruzigana Giriwanyu | 18 | 174 |
| Kigali | Vanessa Raissa Uwase | 22 | 171 |
| Kigali | Belyse Hitayezu | 20 | 179 |
| Kigali | Jane Mutoni | 18 | 171 |
| Eastern Province | Lynca Akacu | 18 | 180 |
| Eastern Province | Fiona Mutoni Naringwa | 20 | 170 |
| Eastern Province | Balbine Mutoni | 18 | 170 |

## Judges

* Cynthia Akazuba - Miss Kigali 2007 and Miss East Africa 2009
* Intore Massamba - Singer and musician
* John Bunyeshuli - Founder of Kigali Fashion Week
* Blanche Majoro - Fashion critic

## Crossovers

Contestants who previously competed at other national beauty pageants:

### Miss Rwanda

* 2014 : Western Province: Vanessa Mpogazi
* 2016 : Western Province: Vanessa Mpogazi (2nd Runner-up)
Contestants who previously competed or will be competing at international beauty pageants:

### Miss Heritage Global

* 2015: Southern Province: Joannah Keza Bagwire (4th Runner-up)