ArticleOriginal scientific text

Title

Analytic gaps

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
  2. Matematicki Institut, Kneza Mihaila 35, 11000 Beograd, Yugoslavia

Abstract

We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.

Bibliography

  1. A. Blass, Near coherence of filters II: Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideal of sequences, and slenderness of groups, Trans. Amer. Math. Soc. 300 (1987), 557-581.
  2. J. Bourgain, Some remarks on compact sets of first Baire class, Bull. Soc. Math. Belg. 30 (1978), 3-10.
  3. J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Baire-measurable functions, Amer. J. Math. 100 (1978), 845-886.
  4. H. G. Dales and W. H. Woodin, An Introduction to Independence for Analysts, Cambridge University Press, 1978.
  5. P. du Bois-Reymond, Eine neue Theorie der Convergenz und Divergenz von Reihen mit positiven Gliedern, J. Reine Angew. Math. 76 (1873), 61-91.
  6. Q. Feng, Homogeneity for open partitions of reals, Trans. Amer. Math. Soc. 339 (1993), 659-684.
  7. D. H. Fremlin, The partially ordered sets of measure theory and Tukey's ordering, Note Mat. 11 (1991), 177-214.
  8. D. H. Fremlin and S. Shelah, On partitions of the real line, Israel J. Math. 32 (1979), 299-304.
  9. D. C. Gillespie and W. A. Hurwitz, On sequences of continuous functions having continuous limits, Trans. Amer. Math. Soc. 32 (1930), 527-543.
  10. J. Hadamard, Sur les caractères de convergence des séries à termes positifs et sur les fonctions indéfiniment croissantes, Acta Math. 18 (1894), 319-336.
  11. F. Hausdorff, Die Graduierung nach dem Endverlauf, Abh. Königl. Sächs. Gesell. Wiss. Math.-Phys. Kl. 31 (1909), 296-334.
  12. F. Hausdorff, Summen von 1 Mengen, Fund. Math. 26 (1936), 241-255.
  13. W. Hurewicz, Relativ Perfekte Teile von Punktmengen und Mengen (A), Fund. Math. 12 (1928), 78-109.
  14. A. S. Kechris, Classical Descriptive Set Theory, Springer, 1995.
  15. A. S. Kechris, A. Louveau and W. H. Woodin, The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), 263-288.
  16. A. Krawczyk, Rosenthal compactum and analytic sets, Proc. Amer. Math. Soc. 115 (1992), 1095-1100.
  17. K. Kunen, Some comments on box products, in: Infinite and Finite Sets, Keszthely 1973, Colloq. Math. Soc. János Bolyai 10, North-Holland, Amsterdam, 1975, 1011-1016.
  18. K. Kunen, (κ,λ*) gaps under MA, note of August 1976.
  19. K. Kunen, An Introduction to Independence Proofs, North-Holland, 1980.
  20. C. Laflamme, Bounding and dominating number of families of functions on ω, Math. Logic Quart. 40 (1994), 207-223.
  21. N. Luzin, On parts of the natural series, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 714-722 (in Russian).
  22. R. Pol, On pointwise and weak topology in function spaces, preprint, Uniw. Warszawski, 1984.
  23. R. Pol, Note on pointwise convergence of sequences of analytic sets, Mathematika 36 (1989), 290-300.
  24. H. P. Rosenthal, Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc. 84 (1978), 803-831.
  25. S. Shelah, Cardinal Arithmetic, Oxford University Press, 1995.
  26. W. Szlenk, The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces, Studia Math. 30 (1968), 53-61.
  27. S. Todorčević, Partition Problems in Topology, Amer. Math. Soc., Providence, 1989.
  28. Z. Zalcwasser, Sur une propriété du champ des fonctions continues, Studia Math. 2 (1930), 63-67.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm150/fm15016.pdf

Pages:
55-66
Main language of publication
English
Received
1995-09-25
Published
1996
Exact and natural sciences