Chains and antichains in Boolean algebras
Fundamenta Mathematicae (2000)
- Volume: 163, Issue: 1, page 55-76
- ISSN: 0016-2736
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top- [1] U. Abraham and S. Shelah, Martin’s axiom does not imply that every two -dense sets of reals are isomorphic, Israel J. Math. 38 (1981), 161-176. Zbl0457.03048
- [2] J. E. Baumgartner, Chains and antichains in P(ℕ), J. Symbolic Logic 45 (1980), 85-92. Zbl0437.03027
- [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. Zbl0452.03044
- [5] R. Bonnet and S. Shelah, Narrow Boolean algebras, Ann. Pure Appl. Logic 28 (1985), 1-12. Zbl0563.03035
- [6] B. Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941), 600-610. Zbl0025.31002
- [7] D. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984. Zbl0551.03033
- [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. Zbl0132.26202
- [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. Zbl0849.03038
- [12] S. Shelah, Decomposing uncountable squares to countably many chains, J. Combin. Theory Ser. A 21 (1976), 110-114. Zbl0366.04009
- [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. Zbl0472.03042
- [14] W. Sierpiński, Sur un problème de la théorie des relations, Ann. Scuola Norm. Sup. Pisa (2) 2 (1933), 285-287. Zbl0007.09702
- [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. Zbl0583.54003
- [17] S. Todorčević, Remarks on cellularity in products, ibid. 57 (1986), 357-372. Zbl0616.54002
- [18] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294. Zbl0658.03028
- [19] S. Todorčević, Irredundant sets in Boolean algebras, Trans. Amer. Math. Soc. 339 (1993), 35-44. Zbl0781.06010