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Completion of factor algebras of ideals


Authors: B. Balcar and F. Franek
Journal: Proc. Amer. Math. Soc. 100 (1987), 205-212
MSC: Primary 06E05; Secondary 03E05, 03G05, 04A20
DOI: https://doi.org/10.1090/S0002-9939-1987-0884452-2
MathSciNet review: 884452
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Abstract: Let $ \mathfrak{I}$ be a $ \kappa $-complete ideal over $ \kappa $. The structure of the completion of the Boolean algebra $ \wp (\kappa)/\mathfrak{I}$ is investigated with respect to properties of the ideal $ \mathfrak{I}$ and the cardinal $ \kappa $. It is shown that under certain conditions $ \operatorname{Comp}(\wp (\kappa )/\mathfrak{I})$ is isomorphic to a collapse algebra.


References [Enhancements On Off] (What's this?)

  • [BPS] B. Balcar, J. Pelant and P. Simon, The space of ultrafilters on $ N$ covered by nowhere dense sets, Fund. Math. 110 (1980), 11-24. MR 600576 (82c:54003)
  • [BSV] B. Balcar, P. Simon and P. Vojtáš, Refinement properties and extensions of filters in Boolean algebras, Trans. Amer. Math. Soc. 267 (1981), 265-283. MR 621987 (82k:06014)
  • [BTW] J. E. Baumgartner, A. D. Taylor and S. Wagon, Ideals on uncountable cardinals, Logic Colloquium 77, Proc. Conf. Wroclaw, 1977.
  • [BV] B. Balcar and P. Vopěnka, On systems of almost disjoint sets, Bull. Acad. Polon. Sci. Sér. Sci. Tech. 20 (1972). MR 0314618 (47:3169)
  • [BVo] B. Balcar and P. Vojtáš, Almost disjoint refinement of families of subsets of $ N$, Proc. Amer. Math. Soc. 79 (1980), 465-470. MR 567994 (81e:04004)
  • [F] F. Franek, Some results about saturated ideals and about isomorphisms of $ \kappa $-trees, Ph.D. Dissertation, Dept. of Math., University of Toronto, 1983.
  • [J] T. Jech, Set theory, Academic Press, 1978. MR 506523 (80a:03062)
  • [JP] T. Jech and K. Prikry, Ideals over uncountable sets: applications of almost disjoint functions and generic ultrapowers, Mem. Amer. Math. Soc., No. 214 (1979). MR 519927 (80f:03059)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0884452-2
Article copyright: © Copyright 1987 American Mathematical Society

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