Cardinal invariants of ultraproducts of Boolean algebras

• Autorzy: Andrzej Rosłanowski , Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 06E15: Stone spaces (Boolean spaces) and related structures
• 03E05: Other combinatorial set theory
• 03E35: Consistency and independence results
• 03G05: Boolean algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 2
• Strony: 101-151

Daty

wydano

1998

otrzymano

1994-12-27

poprawiono

1996-12-06

poprawiono

1997-04-07

Twórcy

autor

Andrzej Rosłanowski

• Mathematical Institute, Wrocław University, 50-384 Wrocław, Poland
• Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel

autor

Saharon Shelah

• Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel

Bibliografia

• [Ko] S. Koppelberg, Handbook of Boolean Algebras, Vol. 1, D. Monk, and R. Bonet (eds.), North-Holland, 1989.
• [KoSh 415] S. Koppelberg, and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145.
• [MgSh 433] M. Magidor and S. Shelah, Length of Boolean algebras and ultraproducts, preprint.
• [Mo 1] D. Monk, Cardinal Invariants of Boolean Algebras, Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1990.
• [Mo 2] D. Monk, Cardinal Invariants of Boolean Algebras, Progr. Math. 142, Birkhäuser, Basel, 1996.
• [Mo 3] D. Monk, Some problems and solutions concerning cardinal functions on Boolean algebras, preprint, 1993.
• [Mo 4] D. Monk, Independence in Boolean algebras, Period. Math. Hungar. 14 (1983), 269-308.
• [Pe] D. Peterson, Cardinal functions on ultraproducts of Boolean algebras, J. Symbolic Logic 62 (1997), 43-59.
• [RoSh 599] A. Rosłanowski and S. Shelah, More on cardinal invariants of Boolean algebras, preprint.
• [Sh 95] S. Shelah, Canonization theorems and applications, J. Symbolic Logic 46 (1981), 345-353.
• [Sh 345] S. Shelah, Products of regular cardinals and cardinal invariants of products of Boolean algebras, Israel J. Math. 70 (1990), 129-187.
• [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.
• [Sh 410] S. Shelah, More on cardinal arithmetic, Arch. Math. Logic 32 (1993), 399-428.
• [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114.
• [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.