| 31. | This axiom schema was tacitly used in the early days of naive set theory, before a strict axiomatization was adopted.
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| 32. | "' Strong collection schema "': This is the constructive replacement for the axiom schema of replacement.
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| 33. | Each of these patterns is an " axiom schema ", a rule for generating an infinite number of axioms.
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| 34. | In other words, if the relation \ phi represents a definable function f, A represents its axiom schema of collection.
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| 35. | An inference rule containing no premises is called an axiom schema or, if it contains no metavariables, simply an axiom.
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| 36. | Such an axiom schema allows infinitely many axioms having a common form to be written as a finite expression connoting that form.
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| 37. | Note that adopting this as an axiom schema will not replace the axiom of union, which is still needed for other situations.
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| 38. | Because the axiom schema of separation is not independent, it is sometimes omitted from contemporary statements of the Zermelo-Fraenkel axioms.
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| 39. | Thus the laws listed below are actually axiom schemas, that is, they stand in place of an infinite number of instances.
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| 40. | The formal version of this axiom resembles the axiom schema of replacement, and embodies the class function " F ".
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