## Axiomatic Set Theory: Impredicative Theories of Classes, Issue 51 |

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### Contents

GENERAL CLASS THEORY | 11 |

MORSEKELLEYTARSKI CLASS THEORY | 121 |

MORSEKELLEYTARSKI CLASS THEORY WITH CHOICE | 319 |

BERNAYS CLASS THEORY | 351 |

377 | |

Index of Symbols | 381 |

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### Common terms and phrases

Applying Ax Class Ax Ext Ax GC Ax Pow Ax Reg axiom of choice biunique cardinal numbers Cartesian product clear closed unbounded cofinal completely additive contradicting COROLLARY deduce define by recursion DEFINITION dense ordering easy to show elements equipollent equivalence relation equivalent exponentiation filter finite following theorem formula function that enumerates Hence implication from left implies impredicative inaccessible inaccessible cardinals induction hypothesis infinite initial ordinals isomorphic least upper bound Let F limit ordinal multiplication n-ary natural numbers obtain order to prove proof is left proper class properties prove by induction reader recursion relation right to left satisfies shown by induction simple ordering stationary strictly increasing subclasses subset Suppose THEOREM SCHEMA transitive transitive set unary operation variables vbtos weakly compact weakly compact cardinals well-ordering WO(R xn_1