Ideals induced by Tsirelson submeasures
Farah, Ilijas
Fundamenta Mathematicae, Tome 159 (1999), p. 243-258 / Harvested from The Polish Digital Mathematics Library

We use Tsirelson’s Banach space ([2]) to define an Fσ P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212332
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     title = {Ideals induced by Tsirelson submeasures},
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     year = {1999},
     pages = {243-258},
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Farah, Ilijas. Ideals induced by Tsirelson submeasures. Fundamenta Mathematicae, Tome 159 (1999) pp. 243-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv159i3p243bwm/

[00000] [1] P. G. Casazza, W. B. Johnson and L. Tzafriri, On Tsirelson's space, Israel J. Math. 47 (1984), 81-98.

[00001] [2] P. G. Casazza and T. J. Shura, Tsirelson's Space, Lecture Notes in Math. 1363, Springer, 1980. | Zbl 0709.46008

[00002] [3] I. Farah, Analytic quotients, to appear. | Zbl 0966.03045

[00003] [4] I. Farah, Analytic ideals and their quotients, PhD thesis, University of Toronto, 1997.

[00004] [5] I. Farah, Basis problem for turbulent actions, preprint, 1998.

[00005] [6] W. T. Gowers, Recent results in the theory of infinite-dimensional Banach spaces, in: Proc. Internat. Congress of Mathematicians, Zürich 1994, Birkhäuser, 1995, 932-942. | Zbl 0868.46004

[00006] [7] G. Hjorth, Actions by classical Banach spaces, J. Symbolic Logic, to appear.

[00007] [8] G. Hjorth and A. S. Kechris, New dichotomies for Borel equivalence relations, Bull. Symbolic Logic 3 (1997), 329-346.

[00008] [9] A. S. Kechris, Rigidity properties of Borel ideals on the integers, Topology Appl. 85 (1998), 195-205. | Zbl 0926.03057

[00009] [10] A. Louveau, On the size of quotients by definable equivalence relations, in: Proc. Internat. Congress of Mathematicians, Zürich 1994, Birkhäuser, 1995, 269-276. | Zbl 0847.04003

[00010] [11] K. Mazur, Fσ-ideals and ω1ω1*-gaps in the Boolean algebra P(ω)/I, Fund. Math. 138 (1991), 103-111.

[00011] [12] K. Mazur, Towards the dichotomy for Fσ-ideals, preprint, 1996.

[00012] [13] E. Odell and T. Schlumprecht, Distortion and stabilized structure in Banach spaces; New geometric phenomena for Banach and Hilbert spaces, in: Proc. Internat. Congress of Mathematicians, Zürich 1994, Birkhäuser, 1995, 955-965. | Zbl 0868.46010

[00013] [14] M. R. Oliver, Borel upper bounds for the Louveau-Veličković and Mazur towers, preprint, 1998.

[00014] [15] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.

[00015] [16] S. Solecki, personal communication, 1997.

[00016] [17] S. Solecki, Analytic ideals, Bull. Symbolic Logic 2 (1996), 339-348. | Zbl 0862.04002

[00017] [18] B. Veličković, Definable automorphisms of P(ω)/fin, Proc. Amer. Math. Soc. 96 (1986), 130-135. | Zbl 0614.03049

[00018] [19] B. Veličković, A note on Tsirelson type ideals, Fund. Math., this issue. | Zbl 0930.03056