## A Theory of SetsThis book provides graduate students and professional mathematicians with a formal unified treatment of logic and set theory. The formalization can be used without change to build just about any mathematical structure on some suitable foundation of definitions and axioms. In addition to most of the topics considered standard fare for set theory several special ones are treated. This book will be found useful as a text for a substantial one-semester course in set theory and that the student will find continuing use for the formal and highly flexible language |

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### Contents

Chapter 0 Language and Inference | 1 |

Chapter 1 Logic | 39 |

Chapter 2 Set Theory | 63 |

Appendix A The Construction of Definitions | 153 |

Appendix B The Consistency of the Axiom of Size | 163 |

Appendix C Axiomatic Equivalence | 167 |

169 | |

173 | |

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### Common terms and phrases

A A ye accepted AGREEMENT AGREENTENT appear Ax ux Ax(ux Ayu'xy binariate Borel F cardinal cblo definiendum definition each expression DEFINITIONAL SCHEMA desired conclusion detachment dmn f empty set Ex ux expressional f scsr F sng formula function is f Hint indicial Induced Rxy Induction Kuratowski's Lemma lemma mathematical nest orderedpair ordinal p a q p v q parenthetical primed symbols Proof reit revised axioms rules of inference schematic expressions schematic substitution schematically replacing set theory sng sng sng x sng xec sngl sorites Step subformula symbol terminal symbol theorem is obtained THEORENAS theory of notation tuple u'xy univalent is f a uſzy ux)e v'xy Vx ux vy ux Vy(ye wellorders x ux xe A A xe Q Zorn's Lemma