Hierarchies and Classifications of Sets 1
نویسنده
چکیده
(2) For every equivalence relation E1 of X and for all sets x, y, z such that z ∈ [x](E1) and z ∈ [y](E1) holds [x](E1) = [y](E1). (3) For every partition P of X and for all sets x, y, z such that x ∈ P and y ∈ P and z ∈ x and z ∈ y holds x = y. (4) For all sets C, x such that C is a classification of X and x ∈ ⋃ C holds x ⊆ X . (5) For every set C such that C is a strong classification of X holds 〈 ⋃ C,⊆〉 is a tree. 1This work has been partially supported by the European Community TYPES grant IST-1999-29001 and CALCULEMUS grant HPRN-CT-2000-00102.
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Hierarchies and Classifications of Sets 1 Mariusz
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