Cardinal invariants of ultraproducts of Boolean algebras

Andrzej Rosłanowski; Saharon Shelah

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 2, page 101-151
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Rosłanowski, Andrzej, and Shelah, Saharon. "Cardinal invariants of ultraproducts of Boolean algebras." Fundamenta Mathematicae 155.2 (1998): 101-151. <http://eudml.org/doc/212247>.

@article{Rosłanowski1998,
abstract = {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.},
author = {Rosłanowski, Andrzej, Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {ultraproducts; cardinal invariants on Boolean algebras},
language = {eng},
number = {2},
pages = {101-151},
title = {Cardinal invariants of ultraproducts of Boolean algebras},
url = {http://eudml.org/doc/212247},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Rosłanowski, Andrzej
AU - Shelah, Saharon
TI - Cardinal invariants of ultraproducts of Boolean algebras
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 2
SP - 101
EP - 151
AB - 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.
LA - eng
KW - ultraproducts; cardinal invariants on Boolean algebras
UR - http://eudml.org/doc/212247
ER -

References

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  1. [Ko] S. Koppelberg, Handbook of Boolean Algebras, Vol. 1, D. Monk, and R. Bonet (eds.), North-Holland, 1989. 
  2. [KoSh 415] S. Koppelberg, and S. Shelah, Densities of ultraproducts of Boolean algebras, Canad. J. Math. 47 (1995), 132-145. Zbl0827.06008
  3. [MgSh 433] M. Magidor and S. Shelah, Length of Boolean algebras and ultraproducts, preprint. 
  4. [Mo 1] D. Monk, Cardinal Invariants of Boolean Algebras, Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1990. 
  5. [Mo 2] D. Monk, Cardinal Invariants of Boolean Algebras, Progr. Math. 142, Birkhäuser, Basel, 1996. Zbl0849.03038
  6. [Mo 3] D. Monk, Some problems and solutions concerning cardinal functions on Boolean algebras, preprint, 1993. 
  7. [Mo 4] D. Monk, Independence in Boolean algebras, Period. Math. Hungar. 14 (1983), 269-308. Zbl0505.03029
  8. [Pe] D. Peterson, Cardinal functions on ultraproducts of Boolean algebras, J. Symbolic Logic 62 (1997), 43-59. Zbl0883.03032
  9. [RoSh 599] A. Rosłanowski and S. Shelah, More on cardinal invariants of Boolean algebras, preprint. 
  10. [Sh 95] S. Shelah, Canonization theorems and applications, J. Symbolic Logic 46 (1981), 345-353. Zbl0472.03043
  11. [Sh 345] S. Shelah, Products of regular cardinals and cardinal invariants of products of Boolean algebras, Israel J. Math. 70 (1990), 129-187. Zbl0722.03038
  12. [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. 
  13. [Sh 371] S. Shelah, Advanced: cofinalities of reduced products, ibid., Chapter VIII. Zbl0654.03037
  14. [Sh 400] S. Shelah, Cardinal arithmetic, ibid., Chapter IX. 
  15. [Sh 410] S. Shelah, More on cardinal arithmetic, Arch. Math. Logic 32 (1993), 399-428. Zbl0799.03052
  16. [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114. Zbl0864.03032
  17. [Sh 460] S. Shelah, The Generalized Continuum Hypothesis revisited, ibid., submitted. Zbl0955.03054
  18. [Sh 462] S. Shelah, σ-Entangled linear orders and narrowness of products of Boolean algebras, Fund. Math. 153 (1997), 199-275. 
  19. [Sh 479] S. Shelah, On Monk's questions, ibid. 151 (1996), 1-19. 
  20. [Sh 503] S. Shelah, The number of independent elements in the product of interval Boolean algebras, Math. Japon. 39 (1994), 1-5. 
  21. [Sh 620] S. Shelah, Special subsets of c f ( μ ) μ , Boolean algebras and Maharam measure algebras, preprint. 

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