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1997 | 153 | 3 | 199-275
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
153
Numer
3
Strony
199-275
Opis fizyczny
Daty
wydano
1997
otrzymano
1994-06-26
poprawiono
1996-12-17
Twórcy
  • Institute of Mathematics, The Hebrew University, 91 904 Jerusalem, Israel
  • Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854, U.S.A.
Bibliografia
  • [ARSh 153] U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of $ℵ_1$-dense real order types, Ann. Pure Appl. Logic 29 (1985), 123-206.
  • [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.
  • [Bo] R. Bonnet, Sur les algèbres de Boole rigides, PhD thesis, Université Lyon 1, 1978.
  • [BoSh 210] R. Bonnet and S. Shelah, Narrow Boolean algebras, Ann. Pure Appl. Logic 28 (1985), 1-12.
  • [CK] C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, Amsterdam, 1973.
  • [EK] R. Engelking and M. Karłowicz, Some theorems of set theory and their topological consequences, Fund. Math. 57 (1965), 275-285.
  • [HLSh 162] B. Hart, C. Laflamme and S. Shelah, Models with second order properties, V: A General principle, Ann. Pure Appl. Logic 64 (1993), 169-194.
  • [MgSh433] M. Magidor and S. Shelah, Length of Boolean algebras and ultraproducts, preprint.
  • [M1] D. Monk, Cardinal Invariants of Boolean Algebras, Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1990.
  • [M2] D. Monk, Cardinal Invariants of Boolean Algebras, Progr. Math. 142, Birkhäuser, Basel, 1996.
  • [RoSh 534] A. Rosłanowski and S. Shelah, Cardinal invariants of ultrapoducts of Boolean algebras, Fund. Math., to appear.
  • [RoSh 599] A. Rosłanowski and S. Shelah, More on cardinal functions on Boolean algebras, preprint.
  • [SaSh 553] O. Shafir and S. Shelah, More on entangled linear orders, preprint.
  • [Sh 620] S. Shelah, On measure algebra, in: Proc. Conf. Prague 1996, submitted.
  • [Sh 460] S. Shelah, The Generalized Continuum Hypothesis revisited, Israel J. Math., submitted.
  • [Sh 50] S. Shelah, Decomposing uncountable squares to countably many chains, J. Combin. Theory Ser. A 21 (1976), 110-114.
  • [Sh 345] S. Shelah, Products of regular cardinals and cardinal invariants of products of Boolean algebras, Israel J. Math. 70 (1990), 129-187.
  • [Sh 410] S. Shelah, More on Cardinal Arithmetic, Arch. Math. Logic 32 (1993), 399-428.
  • [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.
  • [Sh 400] S. Shelah, Cardinal arithmetic, Chapter IX of [Sh g].
  • [Sh 345b] S. Shelah, Entangled orders and narrow Boolean algebras, Appendix 2 to [Sh g].
  • [Sh 405] S. Shelah, Vive la différence II. The Ax-Kochen isomorphism theorem, Israel J. Math. 85 (1994), 351-390.
  • [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114.
  • [To] S. Todorčević, Remarks on chain conditions in products, Compositio Math. 5 (1985), 295-302.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv153i3p199bwm
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