## The New Encyclopaedia Britannica, Volume 27 |

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Page 229

Thus, the intuitive interpretation of the third

condition on x, P(x), those elements of a for which the condition holds form a set.

It provides for the existence of sets by separating off certain elements of existing ...

Thus, the intuitive interpretation of the third

**axiom**schema is: given a set a and acondition on x, P(x), those elements of a for which the condition holds form a set.

It provides for the existence of sets by separating off certain elements of existing ...

Page 230

An application of the ninth

these in the same sense in which to follows the finite ordinals; using notation from

ordinal arithmetic, it is to2. At this point the iteration process can be repeated.

An application of the ninth

**axiom**schema then yields the ordinal that follows all ofthese in the same sense in which to follows the finite ordinals; using notation from

ordinal arithmetic, it is to2. At this point the iteration process can be repeated.

Page 231

a finite number of

ZF provides an

unavoidable because it is known that no finite subset yields the full system of ...

a finite number of

**axioms**. On the other hand, since the ninth**axiom**or schema ofZF provides an

**axiom**for each formula, ZF has infinitely many**axioms**— which isunavoidable because it is known that no finite subset yields the full system of ...

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#### The New Encyclopaedia Britannica (Encyclopaedia)

User Review - Not Available - Book VerdictFor virtually all its 238 years,Britannica has ruled the shelves as a peerless general encyclopedia. Reviewers have consistently given it high marks for most of the 12 criteria identified inKister's ... Read full review

### Contents

San Francisco | 1 |

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Scandinavian Literature | 10 |

Copyright | |

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