| 1. | Every regular ordinal is the initial ordinal of a cardinal.
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| 2. | The least of these is its initial ordinal.
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| 3. | The ?-th infinite initial ordinal is written \ omega _ \ alpha.
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| 4. | If the axiom of choice holds, every cardinal number has an initial ordinal.
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| 5. | The least ordinal of cardinality ( i . e ., the initial ordinal ) is.
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| 6. | Infinite initial ordinals are limit ordinals.
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| 7. | So as an ordinal, an infinite initial ordinal is an extremely strong kind of limit.
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| 8. | A regular ordinal is always an initial ordinal, though some initial ordinals are not regular.
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| 9. | A regular ordinal is always an initial ordinal, though some initial ordinals are not regular.
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| 10. | An ordinal that is equal to its cofinality is called regular and it is always an initial ordinal.
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