Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Almost disjoint refinement of families of subsets of $ {\bf N}$


Authors: Bohuslav Balcar and Peter Vojtáš
Journal: Proc. Amer. Math. Soc. 79 (1980), 465-470
MSC: Primary 04A20; Secondary 54A25, 54D40
DOI: https://doi.org/10.1090/S0002-9939-1980-0567994-2
MathSciNet review: 567994
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Without any set-theoretic assumptions, we prove that every uniform ultrafilter on the set N of all natural numbers has a Comfort system, that is, an almost disjoint refinement. Moreover, we describe one type of ideal such that the family of all subsets of N that are not contained in it has an almost disjoint refinement.


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

  • [BF] B. Balcar and R. Frankiewicz, Ultrafilters and $ {\omega _1}$-points in $ \beta N - N$ (to appear).
  • [BSV] B. Balcar, P. Simon and P. Vojtáš, Refinement properties and extending of filters in Boolean algebras (to appear). MR 628639 (82h:06019)
  • [BPS] B. Balcar, J. Pelant and P. Simon, The space of ultrafilters on N covered by nowhere dense sets, Fund. Math. (to appear). MR 600576 (82c:54003)
  • [CH] W. W. Comfort and N. B. Hindman, Refining families for ultrafilters, Math. Z. 149 (1976), 189-199. MR 0429573 (55:2585)
  • [vD] E. K. van Douwen, Martin's axiom and pathological points in $ \beta X - X$ (manuscript).
  • [H] S. H. Hechler, Generalization of almost disjointness, c-sets, and the Baire number of $ \beta N - N$, General Topology and Appl. 8 (1978), 93-110. MR 0472520 (57:12217)
  • [Hd] N. B. Hindman, On the existence of $ \mathfrak{c}$-point in $ \beta N - N$, Proc. Amer. Math. Soc. 21 (1969), 277-280. MR 0239565 (39:922)
  • [J] T. J. Jech, Set theory, Academic Press, New York, 1978. MR 506523 (80a:03062)
  • [K] K. Kunen, Letter to the author, Sept. 14, 1978.
  • [KvMM] K. Kunen, J. van Mill and Ch. F. Mills, On nowhere dense closed P-sets (to appear). MR 548097 (80h:54029)
  • [M] A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), 59-111. MR 0491197 (58:10462)
  • [P] R. C. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc. no. 70, 1967. MR 0217056 (36:151)
  • [R] J. Roitman, Almost disjoint strong refinements, Notices Amer. Math. Soc. 22 (1975), A 328.
  • [So] R. C. Solomon, Families of sets and functions, Czechoslovak Math. J. 27 (102) (1977), 556-559. MR 0457218 (56:15429)
  • [Sz] A. Szymanski, On the existence of $ {\aleph _0}$-points, Proc. Amer. Math. Soc. 66 (1977), 128-130. MR 0458395 (56:16598)
  • [T] A. D. Taylor, Regularity properties of ideals and ultrafilters, Ann. Math. Logic 16 (1979), 33-55. MR 530430 (83b:04003)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04A20, 54A25, 54D40

Retrieve articles in all journals with MSC: 04A20, 54A25, 54D40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567994-2
Keywords: Ultrafilter, almost disjoint family, $ {2^\omega }$-point, refinement
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society