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1997 | 153 | 3 | 199-275
Tytuł artykułu

σ-Entangled linear orders and narrowness of products of Boolean algebras

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We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts.
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  • Institute of Mathematics, The Hebrew University, 91 904 Jerusalem, Israel
  • Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854, U.S.A.
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  • [AbSh 106] U. Avraham [Abraham] and S. Shelah, Martin's axiom does not imply that every two $ℵ_1$-dense sets of reals are isomorphic, Israel J. Math. 38 (1981), 161-176.
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  • [MgSh433] M. Magidor and S. Shelah, Length of Boolean algebras and ultraproducts, preprint.
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  • [M2] D. Monk, Cardinal Invariants of Boolean Algebras, Progr. Math. 142, Birkhäuser, Basel, 1996.
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  • [RoSh 599] A. Rosłanowski and S. Shelah, More on cardinal functions on Boolean algebras, preprint.
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  • [Sh 371] S. Shelah, Advanced: cofinalities of small reduced products, Chapter VIII of [Sh g].
  • [Sh 355] S. Shelah, $ℵ_{ω+1}$ has a Jonsson Algebra, Chapter II of [Sh g].
  • [Sh 345a] S. Shelah, Basic: Cofinalities of small reduced products, Chapter I of [Sh g].
  • [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994.
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