OpenLLM-France/wikimedia huggingface dataset:
# Inductive set

    Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty.
In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ$^1$$_n$ formula, for some natural number n, together with a real parameter.
The inductive sets form a boldface pointclass; that is, they are closed under continuous preimages. In the Wadge hierarchy, they lie above the projective sets and below the sets in L(R). Assuming sufficient determinacy, the class of inductive sets has the scale property and thus the prewellordering property.
The term can have a number of different meanings:
* Russell's definition, an inductive set is a nonempty partially ordered set in which every element has a successor. An example is the set of natural numbers N, where 0 is the first element, and the others are produced by adding 1 successively.
* Roitman considers the same construction in a more concrete form: the elements are sets, the empty set $\emptyset$ among them, and the successor of every element $y$ is the set $y\cup \{y\}$. In particular, every inductive set contains the sequence $\emptyset ,\{\emptyset \},\{\emptyset ,\{\emptyset \}\},\{\emptyset ,\{\emptyset \},\{\emptyset ,\{\emptyset \}\}\},\dots$.
* For many other authors (e.g., Bourbaki), an inductive set is a partially ordered set in which every totally ordered subset has an upper bound, i.e., it is a set fulfilling the assumption of Zorn's lemma.
# Kevin Baron

Kevin Baron may refer to:
* Kevin Baron (footballer) (1926–1971), English professional footballer
* Kevin Baron (journalist) (born 1975), American journalist
# Kermia granosa

Kermia granosa is a species of sea snail, a marine gastropod mollusk in the family Raphitomidae.

## Description

The length of the shell attains 6 mm.
The color of the shell is cinereous, with four or five revolving brown lines on the upper whorls and three near the base. The shell contains twelve ribs, rather stout. Tnterstices show small transverse ridges, which form nodules on the ribs. The sinus is large, rounded. The peristome is 6-7 toothed within.

## Distribution

This marine species occurs widely in the Indo-West Pacific: off Taiwan; Tahiti; Samoa; Réunion; Queensland, Australia
# Kermia geraldsmithi

Kermia geraldsmithi is a species of sea snail, a marine gastropod mollusk in the family Raphitomidae.

## Description

The length of the shell varies between 4 mm and 6 mm.

## Distribution

This marine species occurs off KwaZulu-Natal, South Africa
# Kermia maculosa

Kermia maculosa is a species of sea snail, a marine gastropod mollusk in the family Raphitomidae.

## Description

The length of the shell varies between 5 mm and 6 mm; its diameter 2½ mm.
(Original description) The oblong-ovate shell is white, shining and sparsely blotched with dark chestnut-brown. It is longitudinally ribbed and transversely elevately striated. The whorls are convex. The aperture is less than one-half the length of the shell.

## Distribution

This marine species occurs off the Philippines.
# Kermia felina

Kermia felina is a species of sea snail, a marine gastropod mollusc in the family Raphitomidae.

## Description

The length of the shell varies between 5 mm and 10 mm.
The shell is decussated by longitudinal and revolving sculpture. It is yellowish white, with chestnut short longitudinal strigations upon the granules, often upon every alternate rib, interrupted by a central white space, and again painted towards the base. Sometimes this coloring is broken up and more or less dispersed over the surface.

## Distribution

This species occurs off Taiwan, Samoa and Queensland, Australia.
# Kevin Hart: Laugh at My Pain

Kevin Hart: Laugh at My Pain is a 2011 stand-up comedy documentary film, starring comedian Kevin Hart. It features Hart performing a stand-up special at the Nokia Theater at L.A. Live in Downtown Los Angeles, among other material. Taraji P. Henson and RuPaul appear, among others.
# Keshendeh-ye Bala

Keshendeh-ye Bala is a village in Balkh Province in northern Afghanistan.
# Khairapara

Khairapara is a village in Jaunpur, Uttar Pradesh, India.
# Khalidia

Khalidia is a town and commune in the Ben Arous Governorate, Tunisia.
# Kidwell

Kidwell may refer to:

## Persons

* Catherine Kidwell (1921–2002), American novelist and teacher
* Clara Sue Kidwell (born 1941), Native American historian, feminist and author
* David Kidwell (b. 1977), New Zealand professional rugby league player
* Peggy A. Kidwell, American historian of science and museum curator
* Wayne L. Kidwell (b. 1938), American jurist and politician; state attorney general and state senator
* Zedekiah Kidwell (1814–1872), American physician, lawyer, and politician from West Virginia; U.S. representative 1853–57

## Other

* Kidwell Airport, Clark County, Nevada, USA
* Kidwell, West Virginia
# Kidwelly (disambiguation)

Kidwelly is a town in Carmarthenshire, Wales.
Kidwelly may also refer to:

## Places

* Kidwelly Castle, a Norman castle in Kidwelly, Wales
* Kidwelly Priory, a former Benedictine priory in Kidwelly, Wales

## Institutions

* Kidwelly RFC, a rugby club representing Kidwelly, Wales
* Kidwelly Industrial Museum, a museum about the Kidwelly tinplate industry
* Kidwelly Town Council, the town council of Mynydd-y-Garreg, Wales and Kidwelly, Wales

## People

* Maurice de Londres (died 1166), Lord of Kidwelly
* Isabella de Beauchamp (c. 1263–1306), Lady of Kidwelly
* Patrick de Chaworth (died 1283), Lord of Kidwelly and wife of Isabella de Beauchamp

## Transportation

* Kidwelly railway station, a railroad station in Kidwelly, Wales
* Kidwelly and Llanelly Canal, a former canal system in Carmarthenshire, Wales
* Kidwelly Flats Halt railway station, a former British military railroad station in Pembrey, Wales

## Other

* Kidwelly sex cult, a former cult in Kidwelly, Wales
# Kilen (lake)

Kilen Lake is a lake in Jutland.
# Kima

Kima is a genus of spiders in the family Salticidae (jumping spiders).

## Species

As of March 2017, the World Spider Catalog accepted the following species:
* Kima africana Peckham & Peckham, 1902 – South Africa
* Kima atra Wesołowska & Russell-Smith, 2000 – Tanzania
* Kima montana Wesołowska & Szeremeta, 2001 – Kenya
* Kima reimoseri (Lessert, 1927) – Republic of Congo
* Kima variabilis Peckham & Peckham, 1903 – South Africa
# Kima montana

Kima montana is a species of jumping spider in the genus Kima that lives in Kenya. The female was first described by Wanda Wesołowska and Małgorzata Szeremeta in 2001.
# Kimberley Town F.C.

Kimberley Town Football Club was a football club based in Kimberley, Nottinghamshire, England. They joined the Midland League in 1971. They reached the Second Round of the FA Vase three times. In the summer of 2012 the club resigned from the Central Midlands League South Division and folded. Their last manager was ex-pro Paul Rawden.

## History

There are records of teams named Kimberley and Kimberley St John's from the late 19th century, playing in the FA Cup between 1892 and 1908. However, the forerunner to the club, Kimberley YMCA, were first reported of in 1915 when they won the Notts Intermediate Cup. The club disbanded in 1928, but reformed with the purpose of playing friendlies in 1947. In the 1950s Kimberley YMCA joined the Notts Amateur League, winning the division's Senior Knockout Cup in 1954 before becoming league champions the following season. This led to promotion to Central Alliance League Division Two. A year later the club changed name to Kimberley Town. In 1986 the club were founder members of the Supreme Division, but a lack of floodlights meant demotion to the Premier Division four seasons later. In the period following, Kimberley Town spent many seasons in both the Premier and Supreme Divisions, with their best finish being second place in the Supreme Division in the 1997–98 season.

## Records

Central Midlands League Supreme Division
* 2nd – 1997–98
Central Midlands League Premier Division
* 5th – 2004–05
Notts Amateur League Division One
* Winners – 1954–55
* Runners-up – 1953–54
Notts Amateur League Senior Knockout Cup
* Winners – 1953–54
FA Cup
* Preliminary Round – 1995–96, 1996–97
FA Trophy
* 3rd Qualifying Round −1973–74
FA Vase
* 2nd Round – 1980–81, 1981–82, 1986–87
# Kimba

Kimba may refer to:

## People

* Kimba Wood (born 1944), U.S. federal judge
* Évariste Kimba (1926–1966), Republic of the Congo's Prime Minister in 1965

## Places
### South Australia

* Kimba, South Australia, a town and locality
* District Council of Kimba, a local government area
* Kimba Airport

### Elsewhere

* Kimba District, District in the Pool Department of Republic of the Congo
* Kimba Payam, South Sudan

## Other uses

* Kimba language, language in Nigeria
* Kimba the White Lion, a manga and anime series by Osamu Tezuka
# Killyhevlin Hotel

54°19′48″N 7°37′12″W﻿ / ﻿54.330°N 7.620°W﻿ / 54.330; -7.620
Killyhevlin Hotel is a hotel situated 1 km from Enniskillen, County Fermanagh, Northern Ireland, just off the main A4 Dublin Road. It is a four star 70-bedroom hotel, with restaurant, spa, swimming pool and health club, on the shores of Lough Erne, surrounded by private grounds and gardens. The hotel was originally owned by Raymond B McCartney who was also the entrepreneur who began the Lough Erne Hotel, Kesh and the Belmore Court & Motel, Enniskillen. It has been owned and managed by the Watson family since 1976, who began a major expansion and rebranding initiative in 2004.

## Awards

The hotel possesses a four star Quality Standard rating from both the AA and Northern Ireland Tourist Board. In July 2008 the hotel was voted as "Northern Ireland's No.2 Best Place to Stay" by Ulster Television viewers on the Ultimate Ulster show.
In 2008, Rodney Watson, managing director of the hotel was made a Member of the Order of the British Empire (MBE) in recognition for services to tourism over the past 30 years. He had been president of the Northern Ireland Hotels Federation and chairman of Fermanagh Lakeland Tourism.
In June 2011 the hotel won the award for best marketing and sales excellence throughout the provence in the 2011 Northern Ireland Tourism Awards.

## History

Over 250 people were evacuated from the hotel, but the explosion injured 17 people, including members of a wedding party, and destroyed much of the recently refurbished hotel. Over 1,000 lbs of homemade explosives had been packed in a vehicle and left at the hotel. The front of the Killyhevlin Hotel collapsed, scores of parked cars were burned and a 12-foot-wide bomb crater was left near the front door.
# Kim Jin-hee

Kim Jin-hee (Korean: 김진희) is the name of:
* Kim Jin-hi (born 1957), South Korean composer and komungo player
* Kim Jin-hee (footballer) (born 1981), South Korean footballer
* Kim Jin-hee (tennis) (born 1981), South Korean tennis player
# King Edward the Fourth and a Tanner of Tamworth

King Edward the Fourth and a Tanner of Tamworth (Roud 248, Child 273) is an English-language folk song, first published in 1564. Versions of this ballad also exist outside the Child collection. Additional copies can be found at the British Library, the University of Glasgow Library, and the Pepys Library at Magdalene College. These ballads' dates, by estimation of the English Short Title Catalogue, range from the early seventeenth century to as late as 1775. The ballad is most recognized by its opening line: "In summer time, when leaves grow green." Child describes the appeal of this ballad to be centered on the chance meeting with a king, which is also a recurring theme in tales of Robin Hood.

## Synopsis

King Edward, while hunting, espies a tanner riding a mare with a cowhide for a saddle. He tells his men to stay back and goes to ask directions to the town of Drayton Bassett. The tanner offers wrong directions, but Edward knows them to be wrong; then Edward invites the tanner to dine with him in Drayton Bassett. The tanner responds that he has no need of charity; he has more pounds in his purse than the stranger has pence in his. Furthermore, he suspects the stranger of having stolen the lordly raiment he is wearing.
Edward asks the tanner for news. The tanner replies that he has heard nothing save that cowhides are in great demand. Edward then asks to switch horses with the tanner. The tanner replies that he'll do the trade but only for a gold noble (80d). Edward, amused, gives him twenty groats (80d), which raises the tanner's opinion of him a bit. The tanner hands over his mare, throws the cowhide over the king's gilt saddle, and tries to ride home; but the cowhide spooks the king's steed and it throws the tanner onto the ground.
The tanner indignantly demands his mare back. Edward, laughing, replies that he'll do the trade but only for a gold noble. The tanner graciously hands Edward not only his original twenty groats but also twenty more, and invites him to share a drink.
Edward then summons his hunting party from over the hill. The tanner first takes them for a band of outlaws, and then (when he realizes Edward's true identity) trembles in fear of royal punishment; but Edward instead thanks the tanner for his entertainment and for his hospitality, and bestows on him Plumpton Park with its three tenements, worth 300 pounds a year. The tanner, not to be outdone, tells Edward that if the king should ever visit his little shop in Tamworth, he can have his shoes re-leathered for free.
Tune
Though no specific tune is listed on any of the ballads—instead it reads: "To an Excellent new Tune"—it is likely the ballad was sung to the tune "In Summer Time," which, again, was also often set to Robin Hood ballads.
# King's House, Slaidburn

King's House is a Grade II listed building in Slaidburn, Lancashire, England, now used as a youth hostel. It was originally built in the 18th century, although parts of the building date back to the 17th century, as the Black Bull public house. The building remained an inn until 1932 when it was rented to YHA and has remained in use as a youth hostel since then. The official opening took place on 28 August 1932. The name King's House is derived from the King family who owned the village the 17th century and whose descendants, the King-Wilkinson family, still own most of the properties in the village.

## Construction

The building is of stone construction with a render over the stone. The roof and dressings are of sandstone. The frontage buildings have two storeys, the rear extension being a single storey. The south range being slightly higher than the north range. A number of outbuildings form the rear border to the yard, which is paved with setts and contains a block used for re-tyring of wheels.
# Kirsten MacKinnon

Kirsten MacKinnon is a Canadian operatic soprano. A winner of the Metropolitan Opera National Council Auditions in 2017, she has appeared internationally.
She grew up in Vancouver, and studied voice at the Curtis Institute of Music in Philadelphia. At the Philadelphia Opera, she performed the roles of Micaëla in Bizet's Carmen and the Countess Madeleine in Capriccio by Richard Strauss. She was Pamina in Mozart's Die Zauberflöte) for the Canadian Opera Company, and the Countess in his Le nozze di Figaro with the Garsington Opera. Her roles have included Elektra in Mozart's Idomeneo, the title role of Tchaikovsky's Iolanta, Mimì in Puccini's La bohème, and the title role in Janáček's The Cunning Little Vixen.
In Europe, she appeared at the Glyndebourne Festival as Fiordiligi in Mozart's Così fan tutte in 2017, staged by Nicholas Hytner. A reviewer of The Guardian described her as "a vocal star" in an "uncommonly well balanced" quartet of lovers, offering "the high notes and the low notes for Fiordiligi and everything in between". She was Helena in Britten's A Midsummer Night's Dream. In February 2018, she made her debut at the Oper Frankfurt, where she is engaged as a member from the 2018/19 season, as Inès in a new production of Meyerbeer's L'Africaine – Vasco da Gama at the Oper Frankfurt, conducted by Antonello Manacorda, alongside Claudia Mahnke and Michael Spyres in the title roles. The opera is staged as a space mission, and she was described as dramatic and of emotional intensity.
MacKinnon has performed in concert with the Chamber Orchestra of Philadelphia, the Bavarian Radio Orchestra, and the Vancouver Symphony Orchestra, among others.
# Kimberly Severson

Kimberly "Kim" Severson (born August 22, 1973, in Tucson, Arizona) is a highly successful international equestrian. She took several years of dressage lessons before training in eventing, and began with a background in Pony Club. One of her first upper level event horses was Jerry McGerry, whom she took intermediate.
Her most well known mount is the English Thoroughbred gelding Winsome Adante (aka "Dan") owned by Linda Wachtmeister and Plain Dealing Farm. The pair won the Rolex Kentucky Three Day three times, an unmatched feat. Dan was retired in a ceremony at Rolex in 2008.
She currently lives in Keene, Virginia.

## Awards

* 1999 Rolex Kentucky CCI*** First Place with Over the Limit
* USEA's Lady Rider of the Year 2001, 2002, 2004, 2005
* 2002 World Equestrian Games in Jerez, Spain Team Gold with Winsome Adante
* 2002 Rolex Kentucky CCI**** First Place with Winsome Adante
* 2004 Rolex Kentucky CCI**** First Place (full format with steeplechase) with Winsome Adante
* 2004 Athens Olympics Individual Silver Medal and Team Bronze with Winsome Adante
* 2005 Rolex Kentucky CCI**** First Place with Winsome Adante
* 2006 FEI World Equestrian Games 17th Individually with Winsome Adante - Team finished 4th
* 2007 The Fork CICW-*** First Place with Winsome Adante
* 2007 Badminton CCI**** Third Place with Winsome Adante

## CCI5* results

Results :
| Event | Kentucky | Badminton | Luhmühlen | Burghley | Pau | Adelaide |
| 2002 | (Winsome Adante) | | | | | |
| 2003 | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate |
| 2004 | (Winsome Adante) | | | | | |
| 2005 | (Winsome Adante) | | 4th (Royal Venture) | EL (Winsome Adante) | | |
| 2006 | RET (Royal Venture) | | | | | |
| 2007 | | (Winsome Adante) | | | | |
| 2008 | 5th (Tipperary Liadhnan) | | | | | |
| 2009 | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate |
| 2010 | 24th (Tipperary Liadhnan) | | | | | |
| 2011 | 16th (Tipperary Liadhnan) | | | | | |
| 2012-13 | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate |
| 2014 | 11th (Fernhill Fearless) | | | | | |
| 2015 | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate |
| 2016 | RET (Fernhill Fearless) | | | | | |
| 2017 | RET (Cooley Cross Border) | | | | | |
| 2018 | 21st (Cooley Cross Border) | | | | 17th (Cooley Cross Border) | |
| 2019 | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate | Did not participate |
| EL = Eliminated; RET = Retired; WD = Withdrew |||||||||||||
# Kisnémedi

Kisnémedi is a village in Pest county, Hungary.
# Kinsmen Sports Centre

The Kinsmen Sports Centre is a multi-purpose sport and recreation facility located in Edmonton, Alberta, Canada. The land surrounding the facility is called Kinsmen Park, part of Edmonton's city-long North Saskatchewan River valley parks system. Its namesake is the Kinsmen, a service organization. The Kinsmen Sports Centre is owned by the City of Edmonton and operated by the Community Services Department. It was the competition site for the 2005 World Masters Games diving, swimming, synchronized swimming and table tennis.

## Kinsmen Field House

The field house was opened January 3, 1968, and was intended to be the first phase of a multifaceted Kinsmen Village that would eventually include an Olympic-size swimming pool and an indoor/outdoor performing arts theatre. At the time of its creation, it was unique among such facilities in Canada and remains the only such facility in North America which is open to general use.
Kinsmen Field House once hosted concerts by many famous artists, including Led Zeppelin & Vanilla Fudge (1969), Frank Zappa (1971), Manfred Mann & KISS (1974), Kansas (1975), Queen (1975), Wishbone Ash (1975), Max Webster (1977), Rush (1975, 1976 & 1977), The Lillo's (1978), Bob Marley (1979), Gary Numan (1980), Motorhead (1981), Ozzy Osbourne (1981), Girlschool, Iron Maiden and The Scorpions (1982), The Clash (1982), Billy Idol w/Platinum Blonde (1984), KISS (1985) and Uriah Heep (1986).

## Kinsmen Aquatic Centre

In 1976, the Kinsmen Aquatic Centre was added to the facility to serve the 1978 Commonwealth Games. Also added in 1992 was the Keltie Byrne Fitness Centre.
# Kladje, Gorenja Vas–Poljane

Kladje (pronounced) is a dispersed settlement at an elevation of 787 meters above sea level above the right bank of the upper course of the Poljane Sora River in the Municipality of Gorenja Vas–Poljane in the Upper Carniola region of Slovenia.
# Kitty Watson

Kitty Watson (March 14, 1886–March 3, 1967), also called as Catherine Watson, was an American vaudeville comedian, often appearing with her sister Fanny Watson (1885-1970) as The Watson Sisters.

## Biography

Kitty Watson was born on March 14, 1886, in Rochester, New York. During her childhood, she started singing with her sister Fanny . Both began singing in old-style variety. They later became comedians, first in burlesque and then in vaudeville. Both regularly appeared on the Broadway stage and radio as The Watson Sisters.
Kitty Watson acted in II club degli ossessi (1920), La dama dal profumo d'ambra rosa (1920) andII corsaro nero (1921). She also performed at Keith Circuit.

## Films

In 1931 the Vitaphone short-subject studio signed Fanny Watson (the stout one of the sister act) and teamed her with comedienne Thelma White for a series of two-reel slapstick comedies, as a sort of female Laurel and Hardy.
In 1933, the Watson Sisters sang "I'm Playing with Fire" in the Max Fleischer Screen Song cartoon Boilesk.
Kitty Watson died on March 3, 1967, in Buffalo, New York. Fanny died in 1970.
# Klofjell

Klofjell is a mountain of Akershus, in southeastern Norway.
60°18′55″N 10°57′34″E﻿ / ﻿60.31528°N 10.95944°E﻿ / 60.31528; 10.95944
* This article about a mountain, mountain range, or peak in Akershus is a stub. You can help Wikipedia by expanding it.
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