Uniqueness of means in the Cohen model

Damjan Kalajdzievski; Juris Steprāns

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 1, page 49-60
  • ISSN: 0010-2628

Abstract

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We investigate the question of whether or not an amenable subgroup of the permutation group on ℕ can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.

How to cite

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Kalajdzievski, Damjan, and Steprāns, Juris. "Uniqueness of means in the Cohen model." Commentationes Mathematicae Universitatis Carolinae 60.1 (2019): 49-60. <http://eudml.org/doc/294504>.

@article{Kalajdzievski2019,
abstract = {We investigate the question of whether or not an amenable subgroup of the permutation group on $\mathbb \{N\}$ can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.},
author = {Kalajdzievski, Damjan, Steprāns, Juris},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {construction scheme; Knaster hierarchy; Cohen reals},
language = {eng},
number = {1},
pages = {49-60},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Uniqueness of means in the Cohen model},
url = {http://eudml.org/doc/294504},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Kalajdzievski, Damjan
AU - Steprāns, Juris
TI - Uniqueness of means in the Cohen model
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 1
SP - 49
EP - 60
AB - We investigate the question of whether or not an amenable subgroup of the permutation group on $\mathbb {N}$ can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.
LA - eng
KW - construction scheme; Knaster hierarchy; Cohen reals
UR - http://eudml.org/doc/294504
ER -

References

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  2. Dushnik B., Miller E. W., 10.2307/2371374, Amer. J. Math. 63 (1941), no. 3, 600–610. MR0004862DOI10.2307/2371374
  3. Foreman M., 10.1006/jfan.1994.1139, J. Funct. Anal. 126 (1994), no. 1, 7–25. MR1305061DOI10.1006/jfan.1994.1139
  4. Krasa S., 10.1090/S0002-9947-1988-0920164-X, Trans. Amer. Math. Soc. 305 (1988), no. 1, 369–376. MR0920164DOI10.1090/S0002-9947-1988-0920164-X
  5. Paterson A. L. T., Amenability, Mathematical Surveys and Monographs, 29, American Mathematical Society, Providence, 1988. Zbl1106.22008MR0961261
  6. Rosenblatt J., Talagrand M., 10.1112/jlms/s2-24.3.525, J. London Math. Soc. (2) 24 (1981), no. 3, 525–532. MR0635883DOI10.1112/jlms/s2-24.3.525
  7. Yang Z., 10.1016/0022-1236(91)90015-W, J. Funct. Anal. 97 (1991), no. 1, 50–63. MR1105654DOI10.1016/0022-1236(91)90015-W

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