First Sentence:
Abelian category An additive category C, which satisfies the following conditions, for any morphism f Hom (X, Y): (i.) f has a kernel (a morphism i Hom (X, X) such that fi = 0) and a co-kernel (a morphism p Hom (Y, Y) such that pf = 0);
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Key Phrases - Statistically Improbable Phrases (SIPs):
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countable chain condition, sentence symbols, regular topological space, quotient object, limit cardinal, elementary substructure, arithmetical hierarchy, first order language, partial recursive function, cohomology operation, phi function, convex closure
Key Phrases - Capitalized Phrases (CAPs):
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Axiom of Choice, Russell's Paradox, Church-Turing Thesis, Martin's Axiom, Axiom of Extensionality, Euclid's Elements, Axiom of Determinacy, Axiom of Union, Axiom of Comprehension
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