Арифметика Пресбургера

Арифметика Пресбургера — это теория первого порядка, описывающая натуральные числа со сложением, но в отличие от арифметики Пеано, исключающая высказывания относительно умножения. Названа в честь польского математика Мойжеша Пресбургера, который в 1929 году предложил соответствующую систему аксиом в логике первого порядка, а также показал её разрешимость.

Аксиомы

Язык арифметики Пресбургера включает константы 0, 1, одну операцию + и предикат равенства =. Аксиомы имеют вид:

  1. ¬(0 = x + 1)
  2. x + 1 = y + 1 → x = y
  3. x + 0 = x
  4. (x + y) + 1 = x + (y + 1)
  5. (P(0) ∧ (P(x)→P(x + 1))) → P(y), где P — формула первого порядка включающая 0, 1, +, = и одну свободную переменную x.

Следует заметить, что (5) на самом деле не одна аксиома, а схема аксиом, представляющая бесконечное множество аксиом, по одной, для каждой формулы P. (5) является формализацией принципа математической индукции. Она не может быть эквивалентно заменена никакой конечной системой аксиом. Таким образом арифметика Пресбургера не является конечно аксиоматизируемой.

См. также

Литература

  • Н. К. Верещагин, А. Шень. Лекции по математической логике и теории алгоритмов. — МЦНМО, 2002.

Ссылки

  • Online-Proofer Java-апплет, проверяющий формулы арифметики Пресбургера на истинность.  (нем.)

Read other articles:

Ergastolo

Disambiguazione – Se stai cercando altri significati, vedi Ergastolo (disambigua). Foto segnaletica di Burton Phillips, condannato all'ergastolo per una rapina in banca nel 1935 L'ergastolo è una pena detentiva a carattere perpetuo inflitta a chi ha commesso un delitto particolarmente grave. Nel 2013 una sentenza della Corte europea dei diritti dell'uomo ha stabilito che tale pena viola i diritti umani quando la scarcerazione sia espressamente proibita o quando non sia previsto nell'o...

 

 

Angkatan Bersenjata Prancis

Angkatan Bersenjata PrancisForces armées françaises Lambang-lambang cabang layanan Angkatan Bersenjata PrancisAngkatanArmée de TerreMarine NationaleArmée de l'Air et de l'EspaceGendarmerie NationaleGarde NationaleKepemimpinanPanglima Tertinggi Presiden Emmanuel MacronMenteri Pertahanan Florence ParlyKepala Pertahanan Jenderal Thierry BurkhardKekuatan personelUsia penerimaan17,5Wajib militerTidak adaPersonel aktif206.317 personel aktifPersonel cadangan41.050 personel cadanganPers...

 

 

Footballers' Wives: Extra Time

Television series This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Footballers' Wives: Extra Time – news · newspapers · books · scholar · JSTOR (February 2019) (Learn how and when to remove this template message) Footballers' Wives: Extra TimeOpening credits titleAlso known asFootballers' Wives: OvertimeCreat...

Investigator Marine Park

Protected area in South AustraliaInvestigator Marine ParkSouth AustraliaA diver carrying out survey work within the marine park.Investigator Marine ParkNearest town or cityElliston[1]Coordinates33°43′46″S 134°38′44″E / 33.729418°S 134.645482°E / -33.729418; 134.645482[1]Established29 January 2009[2]Area1,185 square kilometres (458 sq mi)[3]: 5 Managing authoritiesDepartment of Environment and WaterW...

 

 

South Anchorage High School

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: South Anchorage High School – news · newspapers · books · scholar · JSTOR (August 2011) (Learn how and when to remove this template message) Public secondary school in Anchorage, Alaska, United StatesSouth Anchorage High SchoolAddress13400 Elmore RoadAnchorage,...

 

 

Matius 25

Matius 25Injil Matius 25:41-46 dalam Papirus 45, yang ditulis sekitar tahun 250 M.KitabInjil MatiusKategoriInjilBagian Alkitab KristenPerjanjian BaruUrutan dalamKitab Kristen1← pasal 24 pasal 26 → Matius 25 (disingkat Mat 25) adalah bagian dari Injil Matius pada Perjanjian Baru dalam Alkitab Kristen, yang diyakini disusun menurut catatan Matius, salah seorang dari Keduabelas Rasul Yesus Kristus.[1][2][3][4] Pasal 24 dan 25 merupakan satu rangkaian K...

Huawei P30

Huawei P30 Huawei P30 Pro Huawei P30 LiteHuawei P30 Pro (sub-versi Huawei P30)PembuatHuaweiSeriHuawei PRilis pertama26 Maret 2019; 5 tahun lalu (2019-03-26)PendahuluHuawei P20PenerusHuawei P40TerkaitHuawei Mate 30TipeSmartphoneFaktor bentukSlateBerat P30: 165 gram (5,8 oz) P30 Pro: 192 gram (6,8 oz) Sistem OperasiOriginal: Android 9.0 Pie Sekarang: Android 10CPUOcta-core (2x 2.6 GHz Cortex A76, 2x 1.92 GHz Cortex A76, 4x 1.8 GHz Cortex A55)GPUMali-G76 MP10Memori6...

 

 

List of Knight's Cross of the Iron Cross recipients (O)

Knight's Cross recipientsAllgradesGrand CrossGolden Oak Leaves, Swordsand DiamondsOak Leaves, Swords and DiamondsOak Leaves and SwordsOakLeaves 1940–41 1942 1943 1944 1945 Foreign Knight'sCross A Ba–Bm Bn–Bz C D E F G Ha–Hm Hn–Hz I J Ka–Km Kn–Kz L M N O P Q R Sa–Schr Schu–Sz T U V W X–Z Foreign  Knight's Cross The Knight's Cross of the Iron Cross (German: Ritterkreuz des Eisernen Kreuzes) and its variants were the highest awards in the military and paramilitary force...

 

 

Sharifate of Mecca

967–1916 state in the Arabian Peninsula Sharifate of Meccaشرافة مكة967–1916 Flag1695 map of the Sharifate of MeccaStatusunder Abbasid Caliphate (967–969)Fatimid Caliphate (969–1171)Zengid Sultanate (1171–1174)Ayyubid Sultanate (1174–1254)Abbasid Caliphate (Mamluk Sultanate) (1254–1517)Ottoman Caliphate (1517–1783)Emirate of Diriyah (1783–1818)Ottoman Caliphate (1818–1916)CapitalMeccaOfficial languagesArabicReligion Zaydi IslamSunni Islam (later)Sharif •...

List of Woolworths Group companies

This article is about the Australian retail company. For retailers of a similar name, see Woolworth. This article uses bare URLs, which are uninformative and vulnerable to link rot. Please consider converting them to full citations to ensure the article remains verifiable and maintains a consistent citation style. Several templates and tools are available to assist in formatting, such as reFill (documentation) and Citation bot (documentation). (August 2022) (Learn how and when to remove this...

 

 

Lampshades on Fire

2014 single by Modest MouseLampshades on FireSingle by Modest Mousefrom the album Strangers to Ourselves ReleasedDecember 15, 2014Recorded2013–14GenreAlternative rock, indie rockLength3:08LabelEpicSongwriter(s)Isaac Brock, Jim Fairchild Jeremiah Green, Russell Higbee, Eric Judy, Joe Plummer, Tom PelosoModest Mouse singles chronology Perpetual Motion Machine (2014) Lampshades on Fire (2014) The Ground Walks, with Time in a Box (2015) Lampshades on Fire is a song by American alternative rock ...

 

 

Armand-Augustin-Louis de Caulaincourt

French diplomat (1773–1827) Grand SquireArmand-Augustin-Louis de Caulaincourtduc de VicenceCaulaincourt as Grand Squire (Grand ecuyer), by Féréol Bonnemaison (1806)Born(1773-12-09)9 December 1773Caulaincourt, FranceDied19 February 1827(1827-02-19) (aged 53)Paris, FranceAllegiance Kingdom of France Kingdom of the French French First Republic First French Empire Bourbon Restoration (1814–1815)Service/branchArmyYears of service1788–1815RankGeneral of di...

Naval Station Pearl Harbor

United States naval base on the island of Oahu, Hawaii Naval Station Pearl Harbor Part of Navy Region HawaiiOahu, Hawaii Naval Station Pearl HarborCoordinates21°20′57″N 157°56′38″W / 21.349270°N 157.943970°W / 21.349270; -157.943970TypeMilitary baseSite informationControlled byUnited States NavySite historyIn use1899–present United States historic placePearl Harbor, U.S. Naval BaseU.S. National Register of Historic PlacesU.S. National Historic L...

 

 

Rockville Centre train crash

1950 accident on the Long Island Rail Road Rockville Centre train crashDetailsDateFebruary 17, 1950; 74 years ago (1950-02-17) 10:43 p.m.LocationRockville Centre, New YorkCoordinates40°39′30″N 73°39′08″W / 40.65833°N 73.65222°W / 40.65833; -73.65222CountryUnited StatesLineMontauk BranchOperatorLong Island Rail RoadIncident typeCollisionCauseSignal passed at dangerStatisticsTrains2Passengers800+Deaths32Injured76–158 On February 17, 1950, ...

 

 

Genre sastra

Artikel ini perlu diwikifikasi agar memenuhi standar kualitas Wikipedia. Anda dapat memberikan bantuan berupa penambahan pranala dalam, atau dengan merapikan tata letak dari artikel ini. Untuk keterangan lebih lanjut, klik [tampil] di bagian kanan. Mengganti markah HTML dengan markah wiki bila dimungkinkan. Tambahkan pranala wiki. Bila dirasa perlu, buatlah pautan ke artikel wiki lainnya dengan cara menambahkan [[ dan ]] pada kata yang bersangkutan (lihat WP:LINK untuk keterangan lebih lanjut...

باولو سانتوس (لاعب كرة قدم برتغالي)

  لمعانٍ أخرى، طالع باولو سانتوس (توضيح). باولو سانتوس (بالبرتغالية: Paulinho Santos)‏    معلومات شخصية الميلاد 21 نوفمبر 1970 (العمر 53 سنة)فيلا دو كوندي  الطول 1.70 م (5 قدم 7 بوصة) مركز اللعب وسط الجنسية البرتغال  معلومات النادي النادي الحالي بورتو (مساعد) مسيرة الش�...

 

 

Azida

Anion azidaGugus fungsi azida Azida adalah sejenis anion dengan rumus kimia N−3. Anion ini merupakan basa konjugat bagi asam hidrazoat. N3- ialah anion linear yang isoelektronik dengan CO2 dan N2O. Dalam teori ikatan valensi, azida dapat dijelaskan dengan beberapa struktur resonansi dan yang terpenting adalah N-=N+=N-. Azida juga adalah gugus fungsional dalam kimia organik, RN3.[1] Penggunaan azida yang utama adalah sebagai pendorong di dalam kantung udara. Preparasi Sumber utama ba...

 

 

.jo

Internet country code top-level domain for Jordan .joIntroduced23 November 1994 (in root zone)TLD typeCountry code top-level domainStatusActiveRegistryMinistry of Digital Economy And EntrepreneurshipSponsorNITCIntended useEntities connected with  JordanActual useUsed by Jordanian companies and organizationsRegistered domains5,686 (2022-12-17)[1]Registration restrictionsMust submit official documentsStructureRegistrations are at second level or at third level beneath second level ...

Action 2012

Coalition of organizations supporting the unification of Moldova and Romania Action 2012Acțiunea 2012Logo of Action 2012Formation17 April 2011; 13 years ago (2011-04-17)FounderGeorge SimionTypeNGOLocationMoldova, RomaniaWebsiteOfficial website Action 2012 (Romanian: Acțiunea 2012), officially Unionist Platform Action 2012[1] (Romanian: Platforma Unionistă Acțiunea 2012) or Civic Platform Action 2012[2] (Platforma Civică Acțiunea 2012), is a coalition of...

 

 

Ilhéu Raso, Tanjung Verde

Ilhéu Rasolanskap RasoIlhéu RasoTampilkan peta Cape VerdeIlhéu RasoTampilkan peta Samudera AtlantikGeografiLokasiSamudra AtlantikKoordinat16°37′0″N 24°35′57″W / 16.61667°N 24.59917°W / 16.61667; -24.59917KepulauanTanjung VerdeLuas5.76 km2Panjang3.6 kmLebar2.8 kmTitik tertinggi164 mPemerintahanNegara Tanjung Verde Raso Lark Bagian utara Raso Ilhéu Raso adalah pulau vulkanik berpenghuni seluas 5,76 kilometer persegi (2,22 mil...