PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 163 | 1 | 55-76
Tytuł artykułu

Chains and antichains in Boolean algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give an affirmative answer to problem DJ from Fremlin's list [8] which asks whether $MA_{ω_1}$ implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.
Słowa kluczowe
Twórcy
autor
  • C.N.R.S. (ESA 753), Université Paris 7, 2, Place Jussieu, 75251 Paris Cedex 05, France, stevo@math.jussieu.fr
Bibliografia
  • [1] U. 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.
  • [2] J. E. Baumgartner, Chains and antichains in P(ℕ), J. Symbolic Logic 45 (1980), 85-92.
  • [3] J. E. Baumgartner, Applications of the proper forcing axiom, in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, 913-959.
  • [4] J. E. Baumgartner and P. Komjáth, Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125-133.
  • [5] R. Bonnet and S. Shelah, Narrow Boolean algebras, Ann. Pure Appl. Logic 28 (1985), 1-12.
  • [6] B. Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941), 600-610.
  • [7] D. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984.
  • [8] D. Fremlin, Problems, version of May, 1998.
  • [9] F. Galvin and B. Jónsson, Distributive sublattices of a free lattice, Canad. J. Math. 13 (1961), 265-272.
  • [10] Dj. Kurepa, Transformations monotones des ensembles partiellement ordonnés, Rev. Cienc. (Lima) 437 (1943), 483-500.
  • [11] J. D. Monk, Cardinal Invariants on Boolean Algebras, Birkhäuser, Basel, 1996.
  • [12] S. Shelah, Decomposing uncountable squares to countably many chains, J. Combin. Theory Ser. A 21 (1976), 110-114.
  • [13] S. Shelah, On uncountable Boolean algebras with no uncountable pairwise comparable or incomparable sets of elements, Notre Dame J. Formal Logic 22 (1984), 301-308.
  • [14] W. Sierpiński, Sur un problème de la théorie des relations, Ann. Scuola Norm. Sup. Pisa (2) 2 (1933), 285-287.
  • [15] S. Todorčević, Trees and linearly ordered sets, in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, 235-293.
  • [16] S. Todorčević, Remarks on chain conditions in products, Compositio Math. 55 (1985), 295-302.
  • [17] S. Todorčević, Remarks on cellularity in products, ibid. 57 (1986), 357-372.
  • [18] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294.
  • [19] S. Todorčević, Irredundant sets in Boolean algebras, Trans. Amer. Math. Soc. 339 (1993), 35-44.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv163i1p55bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.