## Axiomatic Set TheoryJames Earl Baumgartner, D. Donald A. Martin, Sharon Shelah, American Mathematical Society |

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### Contents

Preface | 1 |

Sets of ordinals constructlble from trees and the third | 13 |

Existence of bases Implies the axiom of choice | 31 |

Copyright | |

13 other sections not shown

### Common terms and phrases

amalgamation system antichain assume axiom BREP canonical Cantor choose claim closed unbounded filter closed unbounded set club cofinality construction contradiction Corollary countable define definition disjoint elementary embedding elementary submodel elements exists extension finite ground model Hannequin hence implies indecomposable indiscernibles induction infinite initial segment inner model iterated ultrapower large cardinal Lemma limit ordinal lynx Math maxT measurable cardinal Mitchell order Moschovakis natural numbers normal Note order type partial order partition perfect set forcing pinning pointclass poset Prikry proof of Theorem prove rank(X rational perfect set regular cardinal result Russell Russell's S-lynx satisfies sequence set of order set-Fodor simplified morass Solovay split(q stationary set stationary subset successor cardinal Suppose ultrafilter ultrapower weakly preserves well-founded tree