Analytic gaps

Stevo Todorčević

Fundamenta Mathematicae (1996)

  • Volume: 150, Issue: 1, page 55-66
  • ISSN: 0016-2736

Abstract

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

How to cite

top

Todorčević, Stevo. "Analytic gaps." Fundamenta Mathematicae 150.1 (1996): 55-66. <http://eudml.org/doc/212163>.

@article{Todorčević1996,
abstract = {We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.},
author = {Todorčević, Stevo},
journal = {Fundamenta Mathematicae},
keywords = {orthogonal families of sets of integers; separated families of sets of integers; -gap in Borel algebra; -ideal on ; Borel monotonic transfers of analytic ideals on ; analytic families; perfect Luzin gap; nearness; principle of open coloring},
language = {eng},
number = {1},
pages = {55-66},
title = {Analytic gaps},
url = {http://eudml.org/doc/212163},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Todorčević, Stevo
TI - Analytic gaps
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 1
SP - 55
EP - 66
AB - We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.
LA - eng
KW - orthogonal families of sets of integers; separated families of sets of integers; -gap in Borel algebra; -ideal on ; Borel monotonic transfers of analytic ideals on ; analytic families; perfect Luzin gap; nearness; principle of open coloring
UR - http://eudml.org/doc/212163
ER -

References

top
  1. [0] 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. Zbl0647.03043
  2. [1] J. Bourgain, Some remarks on compact sets of first Baire class, Bull. Soc. Math. Belg. 30 (1978), 3-10. Zbl0414.54011
  3. [2] J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Baire-measurable functions, Amer. J. Math. 100 (1978), 845-886. Zbl0413.54016
  4. [3] H. G. Dales and W. H. Woodin, An Introduction to Independence for Analysts, Cambridge University Press, 1978. 
  5. [4] 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. [5] Q. Feng, Homogeneity for open partitions of reals, Trans. Amer. Math. Soc. 339 (1993), 659-684. Zbl0795.03065
  7. [6] D. H. Fremlin, The partially ordered sets of measure theory and Tukey's ordering, Note Mat. 11 (1991), 177-214. Zbl0799.06004
  8. [7] D. H. Fremlin and S. Shelah, On partitions of the real line, Israel J. Math. 32 (1979), 299-304. Zbl0413.04002
  9. [8] D. C. Gillespie and W. A. Hurwitz, On sequences of continuous functions having continuous limits, Trans. Amer. Math. Soc. 32 (1930), 527-543. Zbl56.0212.03
  10. [9] J. Hadamard, Sur les caractères de convergence des séries à termes positifs et sur les fonctions indéfiniment croissantes, Acta Math. 18 (1894), 319-336. Zbl25.0375.02
  11. [10] F. Hausdorff, Die Graduierung nach dem Endverlauf, Abh. Königl. Sächs. Gesell. Wiss. Math.-Phys. Kl. 31 (1909), 296-334. Zbl40.0446.02
  12. [11] F. Hausdorff, Summen von 1 Mengen, Fund. Math. 26 (1936), 241-255. 
  13. [12] W. Hurewicz, Relativ Perfekte Teile von Punktmengen und Mengen (A), Fund. Math. 12 (1928), 78-109. 
  14. [13] A. S. Kechris, Classical Descriptive Set Theory, Springer, 1995. 
  15. [14] 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. Zbl0633.03043
  16. [15] A. Krawczyk, Rosenthal compactum and analytic sets, Proc. Amer. Math. Soc. 115 (1992), 1095-1100. Zbl0768.04003
  17. [16] 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. [17] K. Kunen, (κ,λ*) gaps under MA, note of August 1976. 
  19. [18] K. Kunen, An Introduction to Independence Proofs, North-Holland, 1980. 
  20. [19] C. Laflamme, Bounding and dominating number of families of functions on ω, Math. Logic Quart. 40 (1994), 207-223. Zbl0835.03015
  21. [20] N. Luzin, On parts of the natural series, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 714-722 (in Russian). 
  22. [21] R. Pol, On pointwise and weak topology in function spaces, preprint, Uniw. Warszawski, 1984. 
  23. [22] R. Pol, Note on pointwise convergence of sequences of analytic sets, Mathematika 36 (1989), 290-300. Zbl0719.54047
  24. [23] H. P. Rosenthal, Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc. 84 (1978), 803-831. Zbl0391.46016
  25. [24] S. Shelah, Cardinal Arithmetic, Oxford University Press, 1995. 
  26. [25] W. Szlenk, The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces, Studia Math. 30 (1968), 53-61. Zbl0169.15303
  27. [26] S. Todorčević, Partition Problems in Topology, Amer. Math. Soc., Providence, 1989. Zbl0659.54001
  28. [27] Z. Zalcwasser, Sur une propriété du champ des fonctions continues, Studia Math. 2 (1930), 63-67. Zbl56.0932.04

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.