Georg Cantor. Temat matematikore zakonisht shfaqen dhe evoluojnë përmes ndërveprimeve midis shumë studiuesve.

Disa grupe themelore me rëndësi qendrore janë grupi bosh (grupi unik që nuk përmban elemente; herë pas in this article quhet grupi i pavlefshëm edhe pse ky emër është i paqartë), bashkësia e numrave natyrorë dhe bashkësia e numrave seriousë .

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The things that you've collected will likely be shown underneath "Vocabulary checklist". if you wish to copy vocabulary objects to the vocabulary trainer, click "Import" during the vocabulary checklist.

Në shumë raste, rezultatet e teorisë klasike të përshkrimeve të përshkrimit kanë versione efektive; në disa raste, rezultatet e reja merren duke provuar së pari versionin efektiv dhe më pas duke e zgjëruar atë ("relativizimin") për ta bërë atë më të zbatueshëm.

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Një grup përshkruhet duke renditur elemente të ndara me presje, ose nga një karakteristikë e elementeve të tij, brenda parantezave . Meqenëse grupet janë objekte, lidhja e anëtarësisë mund të ketë lidhje edhe me grupe.

Topologjia vendosur-teorike studion pyetje të topologjisë së përgjithshme që janë natyrë-teorike ose që kërkojnë metoda të përparuara të teorisë së grupit për zgjidhjen e tyre. Shumë nga këto teorema janë të pavarura nga ZFC, që kërkojnë aksioma më të forta për provën e tyre.

Sistemet më të studiuara të teorisë së grupeve aksiomatike nënkuptojnë se të gjitha grupet formojnë një hierarki kumulative . Sisteme të tilla vijnë në dy shije, ato ontologjia e të cilave përbëhet nga:

m.th. "të detyruara") nga ndërtimi dhe modeli origjinal. Për shembull, ndërtimi i Cohen vendos nënndarje shtesë të numrave natyrorë pa ndryshuar asnjë nga numrat kardinalë të modelit origjinal. Forcimi është gjithashtu një nga dy metodat për të provuar përputhshmërinë relative me metodat finitiste, metoda tjetër është modeli me vlera Boolean .

Një product i brendshëm i teorisë së vendosjes së Zermelo-Fraenkel (ZF) është një klasë kalimtare që përfshin të gjitha rregullat dhe plotëson të gjitha aksiomat e ZF. Shembulli kanonik është universi i konstruktueshëm L i zhvilluar nga Gödel. Një arsye që studimi i modeleve të brendshme është me interes është se mund të përdoret për të provuar rezultatet pinay scandalxxx e qëndrueshmërisë.

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