## Reduced Products, Filters and Boolean Ultrapowers |

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### Contents

Regular medium regular strongly regular | 13 |

Model theory of Boolean ultrapowers | 38 |

FOOTNOTES | 56 |

1 other sections not shown

### Common terms and phrases

a-incomplete filter ae s a B-lim Boolean ultrapowers c+-good filter cardinal cl<k clear complete Boolean algebra complete ultrafilter constructed contains a c+-good Corollary countable chain condition DfuW disjointed set elementarily equivalent elementary embedding elementary substructure fe F feA(B filter contains finite intersection property finite set finitely satisfiable following theorem formulas function f Hence holds Ie In(P In(B induction isomorphism Keisler Kunen language Lemma Let f let H Let t(i Let us assume Let us define mapping multiplicative function multiplicative refinement multiplicativity of g n1 n<w n non-trivial filter notion numbers ordinal ordinary ultrapowers P-limDA partially ordered set partition Prikry Prof proof of Theorem prove REDUCED PRODUCTS refines f regular set regular ultrafilter Remark Strongly inaccessible cardinals strongly regular filters structure subsets t(i)nDf Theorem 12 thesis uniform ultrafilter X-regular