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MATHEMATICS
Set Theory
Axiom Schema of Specification
How the Comprehension Principle Shapes Modern Set Theory by Defining Subsets Safely
23 Jan 2026
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Why does the axiom schema of specification restrict comprehension to subsets of an existing set rather than allowing arbitrary set formation?
To avoid paradoxes like Russell's paradox by ensuring only definable subclasses of existing sets are sets
Because it simplifies the notation used in set theory without affecting consistency
Because it allows the creation of larger sets from smaller ones without restrictions
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