# Ideals induced by Tsirelson submeasures

Fundamenta Mathematicae (1999)

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

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

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