## Abstract Sets and Finite Ordinals: An Introduction to the Study of Set TheoryThis text unites the logical and philosophical aspects of set theory in a manner intelligible both to mathematicians without training in formal logic and to logicians without a mathematical background. It combines an elementary level of treatment with the highest possible degree of logical rigor and precision. 1961 edition. |

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### Contents

OPERATIONS ON CLASSES | 16 |

PART II | 31 |

THE BASIS OF THE SYSTEM | 43 |

Copyright | |

3 other sections not shown

### Other editions - View all

Abstract Sets and Finite Ordinals: An Introduction to the Study of Set Theory G. B. Keene Limited preview - 2007 |

Abstract Sets and Finite Ordinals: An Introduction to the Study of Set Theory G. B. Keene Limited preview - 2012 |

### Common terms and phrases

analogous assertion AxIII AxIII(b3 Axiomatic Set Theory axioms class condition class defined class of normal class of pairs class so defined Class Theorem class whose members Column converse domain DbFnc definition determines a class df the class Df.A Df.B diagram element existence theorem existential quantifier F F F false proposition Figure finite class finite ordinal finite sets formula representing given class identical individual constant infer Lemma Let the class logical constants mathematics matrix means Mozart Mz e G normal k-tuplet ordered pairs parameters Paul Bernays Peano Axioms prefixing the sign proper sub-class propositional function quantifier range of values rebracketing represented as follows representing a false representing a true result of applying schema self-augment set theory standard expression sub-proof c(ii symbol theory of finite tion transitive set true proposition tuplets variables for sets word class x e Ml