Ideals induced by Tsirelson submeasures

Ilijas Farah

Fundamenta Mathematicae (1999)

  • Volume: 159, Issue: 3, page 243-258
  • ISSN: 0016-2736

Abstract

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

How to cite

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Farah, Ilijas. "Ideals induced by Tsirelson submeasures." Fundamenta Mathematicae 159.3 (1999): 243-258. <http://eudml.org/doc/212332>.

@article{Farah1999,
abstract = {We use Tsirelson’s Banach space ([2]) to define an $F_σ$ P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).},
author = {Farah, Ilijas},
journal = {Fundamenta Mathematicae},
keywords = {Borel-cardinality; quotients over Borel equivalence relations; Polish space; Borel ideals; trichotomy conjecture; dichotomy conjecture; Tsirelson's Banach space; -ideal},
language = {eng},
number = {3},
pages = {243-258},
title = {Ideals induced by Tsirelson submeasures},
url = {http://eudml.org/doc/212332},
volume = {159},
year = {1999},
}

TY - JOUR
AU - Farah, Ilijas
TI - Ideals induced by Tsirelson submeasures
JO - Fundamenta Mathematicae
PY - 1999
VL - 159
IS - 3
SP - 243
EP - 258
AB - We use Tsirelson’s Banach space ([2]) to define an $F_σ$ P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).
LA - eng
KW - Borel-cardinality; quotients over Borel equivalence relations; Polish space; Borel ideals; trichotomy conjecture; dichotomy conjecture; Tsirelson's Banach space; -ideal
UR - http://eudml.org/doc/212332
ER -

References

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  3. [3] I. Farah, Analytic quotients, to appear. Zbl0966.03045
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  11. [11] K. Mazur, F σ -ideals and ω 1 ω 1 * -gaps in the Boolean algebra P(ω)/I, Fund. Math. 138 (1991), 103-111. 
  12. [12] K. Mazur, Towards the dichotomy for F σ -ideals, preprint, 1996. 
  13. [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. Zbl0868.46010
  14. [14] M. R. Oliver, Borel upper bounds for the Louveau-Veličković and Mazur towers, preprint, 1998. 
  15. [15] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982. 
  16. [16] S. Solecki, personal communication, 1997. 
  17. [17] S. Solecki, Analytic ideals, Bull. Symbolic Logic 2 (1996), 339-348. Zbl0862.04002
  18. [18] B. Veličković, Definable automorphisms of P(ω)/fin, Proc. Amer. Math. Soc. 96 (1986), 130-135. Zbl0614.03049
  19. [19] B. Veličković, A note on Tsirelson type ideals, Fund. Math., this issue. Zbl0930.03056

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