Download PDF - A dichotomy for P-ideals of countable setsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

A dichotomy for P-ideals of countable sets

Authors 1

Affiliations

  1. Université Paris 7, C.N.R.S., UPRESA 7056, 2, Place Jussieu, 72251 Paris Cedex 05, France

Abstract

A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra P(N)/fin but also on some higher order statements like for example the existence of Jensen square sequences.

Bibliography

  1. U. Abraham and S. Todorčević, Partition properties of ω1 compatible with CH, Fund. Math. 152 (1997), 165-181.
  2. K. J. Devlin, The Yorkshireman's guide to proper forcing, in: Surveys in Set Theory, A. R. D. Mathias (ed.), Cambridge Univ. Press, 1983, 60-105.
  3. F. Hausdorff, Summen von ℵ1 Mengen, Fund. Math. 26 (1936), 241-255.
  4. J. Hirschorn, Random trees under CH, preprint, 1999.
  5. R. B. Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229-308.
  6. R. Laver, Making supercompactness indestructible under κ-directed forcing, Israel J. Math. 29 (1978), 385-388.
  7. S. Shelah, Proper Forcing, Springer, 1982.
  8. S. Todorčević, Trees and linearly ordered sets, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 235-293.
  9. S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294.
  10. S. Todorčević, Partition Problems in Topology, Amer. Math. Soc., Providence, 1989.
  11. S. Todorčević, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993), 130-167.
Fundamenta Mathematicae
2000/166/3
Export to PBN, Opens in new tab
Pages:
251-267
Main language of publication
English
Received
1999-11-17
Published
2000
Exact and natural sciences