Remarks on cellularity in products

Stevo Todorčević

Compositio Mathematica (1986)

  • Volume: 57, Issue: 3, page 357-372
  • ISSN: 0010-437X

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Todorčević, Stevo. "Remarks on cellularity in products." Compositio Mathematica 57.3 (1986): 357-372. <http://eudml.org/doc/89758>.

@article{Todorčević1986,
author = {Todorčević, Stevo},
journal = {Compositio Mathematica},
keywords = {cellularity; cellular number; partition relation; caliber; - chain condition; countable chain condition; ZFC; Cohen or random real; ccc poset; precaliber; generalized S and L space problem; 0-dimensional spaces},
language = {eng},
number = {3},
pages = {357-372},
publisher = {Martinus Nijhoff Publishers},
title = {Remarks on cellularity in products},
url = {http://eudml.org/doc/89758},
volume = {57},
year = {1986},
}

TY - JOUR
AU - Todorčević, Stevo
TI - Remarks on cellularity in products
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 57
IS - 3
SP - 357
EP - 372
LA - eng
KW - cellularity; cellular number; partition relation; caliber; - chain condition; countable chain condition; ZFC; Cohen or random real; ccc poset; precaliber; generalized S and L space problem; 0-dimensional spaces
UR - http://eudml.org/doc/89758
ER -

References

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  1. [0] S. Argyros: On compact spaces without strictly positive measure, Pacific J. Math.105 (1983) 257-272. Zbl0523.54016MR691601
  2. [1] M. Bell: Two Boolean algebras with extreme cellular and compactness properties, Canad. J. Math.35 (1983) 824-838. Zbl0519.06012MR735899
  3. [2] W.W. Comfort and S. Negrepontis: Chain Conditions in Topology, Cambridge University Press (1982). Zbl0488.54002MR665100
  4. [3] E.K. Van Douwen and K. Kunen: L-spaces and S-spaces in P (ω), Topology and its Appl.14 (1982) 143-149. Zbl0507.54009
  5. [4] P. Erdös: Some set-theoretic properties of graphs, Univ. Nac. Tucuman RevistaA3 (1942) 363-367. Zbl0063.01265MR9444
  6. [5] P. Erdös and R. Rado: A problem on ordered sets, J. London Math. Soc.28 (1953) 426-438. Zbl0051.04003MR58687
  7. [6] W.G. Fleissner: Some spaces related to topological inequalities proven by the Erdös-Rado Theorem, Proc. Amer. Math. Soc.71 (1978) 313-320. Zbl0411.54007MR493930
  8. [7] H. Gaifman: Concerning measures on Boolean algebras, Pacific J. Math.14 (1964) 61-73. Zbl0127.02306MR161952
  9. [8] F. Galvin: Chain conditions and products, Fund. Math.108 (1980) 33-48. Zbl0366.04011MR585558
  10. [9] T.J. Jech: Set Theory, Academic Press, New York (1978). Zbl0419.03028
  11. [10] R.B. Jensen and R.M. Solovay: Some applications of almost disjoint sets. In Mathematical logic and Foundations of Set Theory (Y. Bar-Hillel, ed.), pp. 84-104. North-Holland, Amsterdam (1970). Zbl0222.02077MR289291
  12. [11] J.L. Kelley: Measures on Boolean algebras, Pacific J. Math.9 (1959) 1165-1177. Zbl0087.04801MR108570
  13. [12] B. Knaster: Sur une propriété caractéristique de l'ensemble des nombres réels, Mat. Sbornik16 (1945) 281-288. Zbl0060.12509MR14389
  14. [13] K. Kuratowski: Topology I, Academic Press, New York (1966). Zbl0158.40802MR217751
  15. [14] D. Kurepa: Sur la puissance des ensembles partiellement ordonnés, Comptes Rendus Soc. Sci.(Varsovie) 32 (1939) 62-67. 
  16. [15] D. Kurepa: On binary symmetrical relations or graphs, Dissertationes Acad. Sci. et Artium Slovenica4 (1953) 67-92. Zbl0053.22202
  17. [16] D. Kurepa: On an inequality concerning cartesian multiplication, Gen. Topology and Its Relations to Modern Analysis and Algebra, Proc. Symp. Prague (1961) 258-259. Zbl0111.18403MR175792
  18. [17] D. Kurepa: The cartesian multiplication and the cellularity numbers, Publ. Inst. Math. (Beograd) (N. S.) 2 (1962) 121-139. Zbl0127.25003MR177894
  19. [18] E. Marczewski: Sur deux propriétés des classes d'ensembles, Fund. Math.33 (1945) 303-307. Zbl0060.12508MR15448
  20. [19] D.A. Martin and R.M. Solovay: Internal Cohen extensions, Ann. Math. Logic2 (1970) 143-178. Zbl0222.02075MR270904
  21. [20] R. Roitman: Adding a random or a Cohen real, Fund. Math.103 (1979) 47-60. Zbl0442.03034MR535835
  22. [21] J. Roitman: Basic S and L. In Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, Amsterdam (1984). Zbl0594.54001MR776619
  23. [22] M. Rubin and S. Shelah: On the expressibility hierarchy of Magidor-Malitz quantifiers, J. Symbolic Logic48 (1983) 542-557. Zbl0537.03026MR716614
  24. [23] M.E. Rudin: S and L spaces. In Surveys in General Topology, G.M. Reed (ed.), Academic Press, New York (1980) 431-444. Zbl0457.54015MR564109
  25. [24] S. Shelah: Jonsson algebras in successor cardinals, Israel J. Math.30 (1978) 57-64. Zbl0384.03016MR505434
  26. [25] S. Shelah: Proper forcing, Lecture Notes in Math. 940, Springer-Verlag, Berlin (1982). Zbl0495.03035MR675955
  27. [26] W. Sierpiński: Sur l'équivalence de trois propriétése des ensembles abstraits, Fund. Math.2 (1921) 179-88. JFM48.0213.04
  28. [27] W. Sierpiński: Sur une probème de la théorie générale des ensembles, Fund. Math.33 (1945) 299-302. Zbl0060.12510MR15450
  29. [28] J. Steprans: Strong Q-sequences and variations on Martin's axiom, Canadian J. Math.37 (1985), 730-746. Zbl0563.03032MR801424
  30. [29] S. Todorcevic: Trees and subtrees, Abstracts Amer. Math. Soc.1: 2 (1982) 237. 
  31. [30] S. Todorcevic: Remarks on chain conditions in products, Compositio Math.55 (1985) 295-302. Zbl0583.54003MR799818
  32. [31] S. Todorcevic: Forcing positive partition relations, Trans. Amer. Math. Soc.280 (1983) 703-720. Zbl0532.03023MR716846
  33. [32] M.L. Wage: Almost disjoint sets and Martin's axiom, J. Symbolic Logic44 (1979) 313-318. Zbl0421.03042MR540662

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