Łoś–Vaught test

In model theory, a branch of mathematical logic, the Łoś–Vaught test is a criterion for a theory to be complete, unable to be augmented without becoming inconsistent. For theories in classical logic, this means that for every sentence, the theory contains either the sentence or its negation but not both.

Statement

A theory with signature σ is -categorical for an infinite cardinal if has exactly one model (up to isomorphism) of cardinality

The Łoś–Vaught test states that if a satisfiable theory is -categorical for some and has no finite model, then it is complete.

This theorem was proved independently by Jerzy Łoś (1954) and Robert L. Vaught (1954), after whom it is named.

See also

References

  • Enderton, Herbert B. (1972), A mathematical introduction to logic, Academic Press, New York-London, p. 147, MR 0337470.
  • Łoś, Jerzy (1954), "On the categoricity in power of elementary deductive systems and some related problems", Colloquium Mathematicum, 3: 58–62, MR 0061561.
  • Vaught, Robert L. (1954), "Applications to the Löwenheim-Skolem-Tarski theorem to problems of completeness and decidability", Indagationes Mathematicae, 16: 467–472, MR 0063993.

Read other articles:

Опис файлу Опис Герб Подолу Джерело Желіба О.В. Час створення 2010 Автор зображення Желіба О.В. Ліцензія Я, власник авторських прав на цей твір, добровільно передаю його у суспільне надбання. У випадку, якщо це юридично неможливо, надаю право використовувати це зображення з �...

كاستيلا الإحداثيات 38°34′11″N 23°37′52″E / 38.5698°N 23.6312°E / 38.5698; 23.6312  تقسيم إداري  البلد اليونان[1]  خصائص جغرافية ارتفاع 11 متر  عدد السكان  عدد السكان 1416 (2011)  معلومات أخرى منطقة زمنية ت ع م+02:00 (توقيت قياسي)،  وت ع م+03:00 (توقيت صيفي)  رمز جيونيمز 260811...

American animated television series Klunk redirects here. For the animatronic talk-show character, Uncle Klunk, see Aaron Fechter and The Rock-afire Explosion. Dastardly and Muttley in Their Flying MachinesDVD box setGenreComedyCreated by William Hanna Joseph Barbera Written byLarz Bourne, Dalton Sandifer, Michael MalteseDirected by William Hanna Joseph Barbera Voices of Don Messick Paul Winchell Narrated byDon MessickComposerTed NicholsCountry of originUnited StatesNo. of episodes17 (34 Dast...

Delta Mahakam, salah satu daerah di Indonesia yang telah menerapkan budidaya perikanan dengan sistem wanamina.[1] Wanamina atau Silvofishery adalah sistem pertambakan teknologi tradisional yang menggabungkan antara usaha perikanan dengan penanaman bakau, yang diikuti konsep pengenalan sistem pengelolaan dengan meminimalkan input dan mengurangi dampak terhadap lingkungan.[2] Latar belakang Di Asia Tenggara, penerapan sistem wanamina semakin giat untuk digalakkan, hal ini diseba...

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2022. Lulongganda atau Lulo Ngganda adalah sebuah tradisi masyarakat suku Tolaki, desa Benua, kecamatan Benua, kabupaten Konawe Selatan, Sulawesi Tenggara yang merupakan warisan dari budaya leluhur mereka. Lulo berarti goyang dan Ngganda berasal dari kata ka...

Italian tennis player Nicola PietrangeliCountry (sports) ItalyResidenceRome, ItalyBorn (1933-09-11) 11 September 1933 (age 90)Tunis, TunisiaHeight1.78 m (5 ft 10 in)Turned pro1968 (amateur from 1953)Retired1973PlaysRight-handed (one-handed backhand)Int. Tennis HoF1986 (member page)SinglesCareer record687–278 (71.4%) [1]Career titles44Highest rankingNo. 3 (1959, Lance Tingay)[2]Grand Slam singles resultsAustralian OpenQF ...

Russian singer This article is about guitar player. For duduk player, see Armen Grigoryan (duduk player). Armen GrigoryanBackground informationBirth nameArmen Sergeevich GrigoryanBorn (1960-11-24) November 24, 1960 (age 63)Moscow, RSFSR, Soviet UnionGenresRockInstrument(s)Guitar, harmonicaYears active1978-LabelsMelodiya, Moroz, Soyuz, Kvadro-DiskWebsitewww.crematorium.ruMusical artist Armen Grigoryan (Russian: Армен Григорян, Armenian: Արմեն Գրիգորյան) is a sin...

Gambar seorang Beguine dari Des dodes dantz, dicetak di Lübeck tahun 1489. Beguines /bəˈɡiːnz/ dan Beghards /bəˈɡɑːrdz/ adalah tarekat awam Kristen yang aktif di Eropa Utara, khususnya di Negeri-negeri Dataran Rendah pada abad ke-13 hingga ke-16. Anggota tarekat ini tinggal di komunitas setengah monastik, tetapi tidak mengucapkan kaul resmi. Maka dari itu, meskipun mereka berjanji tidak akan menikah selama menjadi Beguines, mereka bebas untuk meninggalkan tarekat mereka kapanpun mer...

Political party in Canada Atlantica Party Active provincial partyLeaderKyle Woodbury[1]Founded2006RegisteredMarch 8, 2010 (original) June 28, 2016 (relaunch)DissolvedJune 5, 2012 (original)Headquarters36 Heritage DriveAntigonish, Nova ScotiaB2G 2T6Membership (2021)100-200[2]IdeologyClassical liberalismLaissez-faire economicsColours   Blue and whiteSeats in House of Assembly0 / 55WebsiteOfficial websitePolitics of Nova ScotiaPolitical partiesElections The Atlantic...

Reference resource produced by the Central Intelligence Agency Not to be confused with Encyclopedia of the Central Intelligence Agency. This article relies excessively on references to primary sources. Please improve this article by adding secondary or tertiary sources. Find sources: The World Factbook – news · newspapers · books · scholar · JSTOR (January 2022) (Learn how and when to remove this template message) The World Factbook Emblem of The World...

1990 video gameUltima VI: The False ProphetDeveloper(s)Origin SystemsPublisher(s)Origin SystemsProducer(s)Richard GarriottWarren SpectorDesigner(s)Richard GarriottSeriesUltimaPlatform(s)MS-DOS, Amiga, Atari ST, Commodore 64, FM Towns, PC-9801, Super NES, X68000ReleaseApril 1990 (DOS)[1]1991–1992 (ports)Genre(s)Role-playingMode(s)Single player Ultima VI: The False Prophet, released by Origin Systems in 1990, is the sixth part in the role-playing video game series of Ultima. It is the...

Награды Пермского края — награды субъекта Российской Федерации учреждённые Законодательным Собранием Пермского края согласно Закону Пермского края от 8 декабря 2013 года № 270-ПК «О наградах Пермского края»[1] и других законодательных актов. Награды Пермского края яв�...

Dutch Golden Age painter Martinus LengeleBorn1615Died27 May 1668ParisNationalityDutch Martinus Lengele (1615–1668) was a Dutch Golden Age painter. The Officers of the Orange Banner in The Hague, 1660, Haags Historisch Museum He is known for portraits in the Hague, and made a few schutterstuken there. He became a member of the Confrerie Pictura in The Hague from 1656 to 1665.[1] In 1642 his sister Anna married the painter Jacob van Loo, who like him, worked in Paris in the 1660s. Len...

Political ideology The flag of the Arab Revolt was originally used against the Ottoman Turks, and remains a prominent symbol of Arab nationalism. The design and pan-Arab colours are the basis of many modern Arab states' flags. Coat of arms (emblem) Hawk of Quraish: It is one of the Arab national symbols that have been used in many Arab nation-states. The Aqaba Flagpole in Aqaba, Jordan bearing the flag of the Arab Revolt. The Aqaba Flagpole is the sixth tallest free standing flagpole in the w...

French actress Pascale PetitPetit in 1960Born (1938-02-27) 27 February 1938 (age 85)Paris, FranceOccupationActressYears active1957-2001 Pascale Petit (born Anne-Marie Pettit;[1] 27 February 1938) is a French actress.[2] She appeared in more than fifty films from 1957 to 2001. Biography Working as a hairdresser, she entered films when her beauty was noticed by actress Françoise Lugagne whose husband Raymond Rouleau was searching for young actresses for his directoria...

Kimia padatan adalah kajian tentang sintesis, struktur, dan sifat-sifat fisik material padat. Jadi, bidang ini mempunyai tumpang-tindih yang kuat dengan fisika padatan, mineralogi, kristalografi, keramik, metalurgi, termodinamika, ilmu material, dan elektronika dengan perhatian pada sintesis material baru dan karakterisasinya. Sejarah penentuan struktur Sebelum abad ke-20, para kimiawan mengalami kesulitan dalam menentukan struktur suatu senyawa. Cara yang dilakukan pada masa itu adalah denga...

American television series TrinketsGenreTeen dramaCreated by Amy Andelson Emily Meyer Kirsten Kiwi Smith Based onTrinketsby Kirsten Kiwi SmithStarring Brianna Hildebrand Kiana Madeira Quintessa Swindell Brandon Butler Odiseas Georgiadis Larry Sullivan Dana Green Linden Ashby October Moore ComposerKeegan DeWittOriginal languageEnglishNo. of seasons2No. of episodes20ProductionExecutive producers Amy Andelson Emily Meyer Linda Gase Kirsten Kiwi Smith Shelley Zimmerman Rebecca Glashow Brin Lukens...

Ice sports complex in Sydney, Australia Liverpool Catholic Club Ice RinkLocationLiverpool Catholic Club Corner Joadja and Hoxton Park Roads, Liverpool West NSW 2170Coordinates33°55′44″S 150°52′30″E / 33.928877°S 150.874883°E / -33.928877; 150.874883Capacity500 (seating)Surface60 m × 30 m (197 ft × 98 ft)Opened1979 (44 years ago) (1979)TenantsLCC Saints Ice Hockey Club (1979-present) Sydney Ice Dogs (2009-2016)We...

Not to be confused with Saifee Hospital, Karachi. Hospital in Maharashtra, IndiaSaifee HospitalGeographyLocation15/17, Maharshi Karve Marg, Charni Road, Mumbai, Maharashtra, IndiaCoordinates18°57′09″N 72°49′05″E / 18.952493°N 72.818177°E / 18.952493; 72.818177 (Saifee Hospital)OrganisationTypeGeneralReligious affiliationDawoodi BohraServicesEmergency departmentYesBeds257HistoryOpened1948LinksWebsitewww.saifeehospital.comListsHospitals in India Saife...

English actor (b. 1971) For other people named James Redmond, see James Redmond (disambiguation). James RedmondBornJames William Forbes Redmond (1971-11-24) 24 November 1971 (age 52)London, EnglandEducationClifton CollegeOccupations Actor model presenter Years active1997–presentChildren1 James William Forbes Redmond (born 24 November 1971) is an English actor, presenter, stand-up comedian and model, known for his roles as Abs Denham in Casualty and Rory Finnigan in Hollyoaks. Care...