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.
Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
Bibliografia
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[KoSh 415] S. Koppelberg, and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145.
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[Mo 1] D. Monk, Cardinal Invariants of Boolean Algebras, Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1990.
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[Sh 355] S. Shelah, $ℵ_ω+1$ 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.
[Sh 371] S. Shelah, Advanced: cofinalities of reduced products, ibid., Chapter VIII.
[Sh 400] S. Shelah, Cardinal arithmetic, ibid., Chapter IX.
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[Sh 460] S. Shelah, The Generalized Continuum Hypothesis revisited, ibid., submitted.
[Sh 462] S. Shelah, σ-Entangled linear orders and narrowness of products of Boolean algebras, Fund. Math. 153 (1997), 199-275.
[Sh 479] S. Shelah, On Monk's questions, ibid. 151 (1996), 1-19.
[Sh 503] S. Shelah, The number of independent elements in the product of interval Boolean algebras, Math. Japon. 39 (1994), 1-5.
[Sh 620] S. Shelah, Special subsets of $^{cf(μ)} μ$, Boolean algebras and Maharam measure algebras, preprint.