## Models of ZF-Set Theory |

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### Contents

Prerequisites 3TAT library | viii |

Constructible Sets | 23 |

FraenkelMostowskiSpecker Models | 46 |

Copyright | |

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### Common terms and phrases

A.LEVY atoms automorphism axiom of choice axiom of foundation axiom of infinity axiom of regularity axiom of replacement Boolean algebra Boolean Prime Ideal cardinality choice AC Cohen-generic constant terms contains Continuum Hypothesis contradiction Corollary countable standard model Dedekind-finite definition elements equivalent exists Feferman finite subset forcing relation free variables function f Godel's Halpern Hence implies independence infinite isomorphic KW-AC lemma lemmata limited comprehension term Math model of ZF Mostowski natural numbers obtained occ(t one-to-one mapping ord(x ordering principle ordinal P.J.COHEN pairwise disjoint partially ordered partially ordered set permutation model pointwise fixed Prime Ideal theorem provable in ZF proved quantifiers reflexive sets result satisfies schema set theory small subtree subgroups of G Suppose symbols syntactic model val(t well-founded set wellorderable wellordering X-formula Zermelo ZF is consistent ZF-formula