## Localization and iteration of axiomatic set theory |

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### Contents

PREFACE | 7 |

INTRODUCTION | 9 |

The axiomatic theory of Chapter I | 11 |

Copyright | |

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91 is locally anti-reflexive atom Axiom Groups axiom of choice axiom of foundation axiomatic set theory axioms of Axiom basic predicates big class Chapter closed formula conclusions of 4.1 consequence of 91 Consider any class continuum hypothesis define dom(ip dom(R easily seen element equipotent equivalent finitely orders following metatheorem following theorem function q function with domain given Hence infinite initial segment inner models intuitive integer isomorphism Lemma limit ordinal locally conservative lower closure maximally joins metaobjects minimum natural number neo-atom neo-class notion object objectp one-one function ordinal number ordinal sum perfectly amenable power class predicates elt Proof proper subclass prove ranking function relative to 91 Remark resp S4 hold semiformula statement subset Suppose B'6 termwise set-like theorem is routine totally orders upper closure vertical closure vertically limited vertically normal well-orders xesi