For example, New Foundations and positive set theory use different restrictions of the axiom of comprehension of naive set theory.
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Another example is positive set theory, where the axiom of comprehension is restricted to hold only for the positive formulas ( formulas that do not contain negations ).
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Syntactic non-standard analysis requires a great deal of care in applying the principle of set formation ( formally known as the axiom of comprehension ), which mathematicians usually take for granted.
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