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Translation examples
The categorical dual of a monomorphism is an epimorphism, i.e. a monomorphism in a category C is an epimorphism in the dual category Cop.
Epimorfismin duaali on monomorfismi, eli epimorfismi kategoriassa C on monomorfismi duaalikategoriassa Cop.
Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the Robinson-Zakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of non-standard analysis, which was pioneered (as an application of the compactness theorem) by Abraham Robinson.
Joitakin ultratulojen hyödyllisyyttä osoittaa hyvin eleganttiselvennä todistus kompaktisuus- ja täydellisyyslauseille, Keislerin ultrapotenssilause, joka antaa algebrallisen karakterisaation elementaarisen ekvivalessin semanttiselle merkinnälle, ja Robinsonin–Zakonin esitys, jossa käytetään superrakenteita ja niiden monomorfismeja konstruoimaan analyysin epästandardeja malleja.selvennä Epästandarin analyysin pioneeri oli Abraham Robinson, joka tutki niitä kompaktisuuslauseen sovelluksena.
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