Cardinal invariants of ultraproducts of Boolean algebras
Rosłanowski, Andrzej ; Shelah, Saharon
Fundamenta Mathematicae, Tome 158 (1998), p. 101-151 / Harvested from The Polish Digital Mathematics Library

We deal with some problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariants of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:212247
@article{bwmeta1.element.bwnjournal-article-fmv155i2p101bwm,
     author = {Andrzej Ros\l anowski and Saharon Shelah},
     title = {Cardinal invariants of ultraproducts of Boolean algebras},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {101-151},
     zbl = {0896.03034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv155i2p101bwm}
}
Rosłanowski, Andrzej; Shelah, Saharon. Cardinal invariants of ultraproducts of Boolean algebras. Fundamenta Mathematicae, Tome 158 (1998) pp. 101-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv155i2p101bwm/

[00000] [Ko] S. Koppelberg, Handbook of Boolean Algebras, Vol. 1, D. Monk, and R. Bonet (eds.), North-Holland, 1989.

[00001] [KoSh 415] S. Koppelberg, and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145. | Zbl 0827.06008

[00002] [MgSh 433] M. Magidor and S. Shelah, Length of Boolean algebras and ultraproducts, preprint.

[00003] [Mo 1] D. Monk, Cardinal Invariants of Boolean Algebras, Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1990.

[00004] [Mo 2] D. Monk, Cardinal Invariants of Boolean Algebras, Progr. Math. 142, Birkhäuser, Basel, 1996. | Zbl 0849.03038

[00005] [Mo 3] D. Monk, Some problems and solutions concerning cardinal functions on Boolean algebras, preprint, 1993.

[00006] [Mo 4] D. Monk, Independence in Boolean algebras, Period. Math. Hungar. 14 (1983), 269-308. | Zbl 0505.03029

[00007] [Pe] D. Peterson, Cardinal functions on ultraproducts of Boolean algebras, J. Symbolic Logic 62 (1997), 43-59. | Zbl 0883.03032

[00008] [RoSh 599] A. Rosłanowski and S. Shelah, More on cardinal invariants of Boolean algebras, preprint.

[00009] [Sh 95] S. Shelah, Canonization theorems and applications, J. Symbolic Logic 46 (1981), 345-353. | Zbl 0472.03043

[00010] [Sh 345] S. Shelah, Products of regular cardinals and cardinal invariants of products of Boolean algebras, Israel J. Math. 70 (1990), 129-187. | Zbl 0722.03038

[00011] [Sh 355] S. Shelah, ω+1 has a Jonsson algebra, Chapter II of Cardinal Arithmetic, Oxford Logic Guides 29, D. M. Gabbai, A. Macintyre and D. Scott (eds.), Oxford University Press, 1994.

[00012] [Sh 371] S. Shelah, Advanced: cofinalities of reduced products, ibid., Chapter VIII. | Zbl 0654.03037

[00013] [Sh 400] S. Shelah, Cardinal arithmetic, ibid., Chapter IX.

[00014] [Sh 410] S. Shelah, More on cardinal arithmetic, Arch. Math. Logic 32 (1993), 399-428. | Zbl 0799.03052

[00015] [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114. | Zbl 0864.03032

[00016] [Sh 460] S. Shelah, The Generalized Continuum Hypothesis revisited, ibid., submitted. | Zbl 0955.03054

[00017] [Sh 462] S. Shelah, σ-Entangled linear orders and narrowness of products of Boolean algebras, Fund. Math. 153 (1997), 199-275.

[00018] [Sh 479] S. Shelah, On Monk's questions, ibid. 151 (1996), 1-19.

[00019] [Sh 503] S. Shelah, The number of independent elements in the product of interval Boolean algebras, Math. Japon. 39 (1994), 1-5.

[00020] [Sh 620] S. Shelah, Special subsets of cf(μ)μ, Boolean algebras and Maharam measure algebras, preprint.