| 21. | Additional examples of inconsistent theories arise from the axiom schema of unrestricted comprehension is assumed in set theory.
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| 22. | These axioms are all axiom schema of induction makes redundant the axioms 3, 10, and 11.
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| 23. | The Hoare axiom for assignment is not given as a single axiom but rather as an axiom schema.
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| 24. | The next four are general statements about second-order induction axiom with a first-order axiom schema.
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| 25. | The axiom schema of specification must be used to reduce this to a set with exactly these two elements.
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| 26. | Axiomatizing arithmetic induction in first-order logic requires an axiom schema containing a separate axiom for each possible predicate.
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| 27. | The axiom schema of collection is equivalent to the axiom schema of replacement over the remainder of the ZF axioms.
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| 28. | The axiom schema of collection is equivalent to the axiom schema of replacement over the remainder of the ZF axioms.
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| 29. | Thus, one may use this as an axiom schema in the place of the axioms of empty set and pairing.
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| 30. | For this reason, the axiom schema of separation is often left out of modern lists of the Zermelo Fraenkel axioms.
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